Your Federal Quarterly Tax Payments are due April 15th Get Help Now >>

SM 1.11.4 Exams by ashrafp

VIEWS: 700 PAGES: 28

									SAV 6 - PROGRAM                                                   OCTOBER 1999



                           MID-TERM EXAMINATION

                                                          Time:
                                                          9:30 AM – 11:30 AM
                 BUSINESS STATISTICS

 Lecturer                 Student ID:                     Date:

 Dr. Ho Thanh Phong       Name:
                                                          October 22, 1999

Instructions:

a. Every question has the same score.
b. For True/False question, a plus for right answer and minus for wrong answer
c. Discussion is strictly prohibited.

                                  Questions

1. Classifying students in a statistics course by their home town is an example
   of what scale of measurement?
   A) Nominal
   B) Ordinal
   C) Interval
   D) Ratio
       Answer:

2. A clothes store manager has sales data of trouser sizes for the last month ’s
   sales. Which measure of central tendency should the manager use, if the
   manager is interested in the most sellable size?
   A) mean
   B) median
   C) mode
   D) standard deviation
   E) interquartile range
      Answer:

3. The mean weight of three gemstones is 12 grams. The weights of two of the
   stones are 9 grams and 11 grams. What is the weight of the third stone?
   A) 16 grams
   B) 10 grams
   C) 8 grams
   D) 14 grams



Business Statistics                     -1-                  Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                      OCTOBER 1999



   E) not enough information to determine the weight of the third stone
       Answer:
Use the following to answer question 4, 5:
The following is the age distribution in a particular building:
            Age                Number of People
            0 – 10                       7
            10 – 20                     10
            20 – 30                     12
            30 – 40                     15
            40 – 50                     11
            50 – 60                      6
            60 – 70                      4
            70 – 80                      2

4. What is the mean age of the people living in this building?
   A) 67.0
   B) 40.0
   C) 33.5
   D) 28.0
   E) none of the above
      Answer:

5. What is the median age of people living in this building?
   A) 32.67
   B) 30
   C) 32.33
   D) 34
   E) 15
      Answer:

6. The following numbers represent the electricity bill each house in a particular
   area received in the past month. $64, 79, 92, 101, 113, 115, 129, 135, 138,
   143, 146, 158, 163, 165, 168, 173, 174, 177, 181, 184, 187, 189, 190, 193,
   196, 200, 205, 218, 231, 249 and 278. What is the 60 th percentile for these
   values?
   A) 190.2
   B) 179.4
   C) 181.6
   D) 182.5
   E) 177
      Answer:

7. A class of business students received the following test scores on a
   standardized test: 320, 410, 440, 470, 480, 480, 490, 500, 500, 510, 510,



Business Statistics                    -2-                       Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                  OCTOBER 1999



    530, 530, 530, 540, 570, 600, 650, 720 and 790. How many students in this
    group received a score that was greater than the 75th percent of this group?
    A) 56
    B) 5
    C) 563
    D) 15
    E) not enough information to answer
       Answer:

Use the following to answer questions 8, 9, 10:
The following are the valuations (in thousands of dollars) of 16 randomly
selected properties sold during the past year:
130 110 130 130 120 140 120 110
150 150 130 140 130 130 120 140

8. Find the mean, median, and mode of these data:
   Answer: Mean:        , Median:          , Mode:

9. Find the variance of the distribution:
   Answer: Variance:

10. Based on Chebyshev’ theorem, what range would you say should include at
    least 75% of property valuations?
    Answer: [           ,             ]

The probability distribution of the number of hours the evening flight from
Chicago to New York is late is found to be as follows:
X          P(X)
1          0.1
2          0.1
3          0.2
4          0.3
5          0.2
6          0.1

11. Find the standard deviation of the flight delay
    A) 2.00
    B) 0.2
    C) 1.4177
    D) 3.7
    E) none of the above
       Answer:

Use the following to answer question 12, 13:



Business Statistics                     -3-                  Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                       OCTOBER 1999



The number of bags per passenger travelling on a particular flight has the
following probability distribution:
X           P(X)
0            0.1
1           0.3
2           0.4
3           0.1
4           0.1

12. What percentage of passengers who have more than one bag?
    A) 60%
    B) 30%
    C) 10%
    D) 90%
    E) 40%
        Answer:
13. What percentage of passengers has at least one bag?
    A) 60%
    B) 30%
    C) 10%
    D) 90%
    E) 40%
        Answer:

Use the following to answer questions 14, 15:
A company has a new project under way and selects five executives for a
transfer from their current jobs. A report had suggested that 75% of all
executives in this company would like this new job.

14. What is the probability that at least three of these five selected like their new
    job?
    A) 0.4219
    B) 0.45
    C) 0.25
    D) 0.5781
    E) 0.8965
         Answer:

15. What is the probability that exactly three of the five selected like their new
    job?
    A) 0.0264
    B) 0.4219
    C) 0.7363
    D) 0.2637



Business Statistics                     -4-                      Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                   OCTOBER 1999



    E) 0.8965
        Answer:
16. A new medicine has an 85% success rate. Five patients are treated with it.
    What is the probability that at least four are cured with this new medicine?
    A) 0.4437
    B) 0.3915
    C) 0.5220
    D) 0.83521
    E) none of the above
        Answer:

17. The arithmetic mean assumes an interval level of measurement.
    A) True
    B) False
      Answer:

18. Chebyshev’s Theorem states that at least 8/9 of the observations in a set
   will lie within 3 standard deviations of the mean.
   A) True
   B) False
       Answer:

19. A record of the numbers of models of each of five models of cars sold by a
    dealership during the past 18 months is an example of ordinal data.
    A) True
    B) False
        Answer:

20. A random variable is discrete if it can assume only certain values within its
    range.
    A) True
    B) False
        Answer:

21. In a binomial experiment with n= 50 trials, and the probability of success on
    each trial equal to 0.2, the expected value of the random variable is 40.
    A) True
    B) False
         Answer:

22. The probability that a standard normal random variable will have a value of
    ten is very close to one.
    A) True
    B) False



Business Statistics                   -5-                     Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                  OCTOBER 1999



         Answer:

23. The probability that a normal random variable will be within two standard
    deviations of its mean is approximately 0.68.
    A) True
    B) False
        Answer:

24. A calculator manufacturer performs a test on its calculators and finds their
    working life to be normally distributed, with a mean of 2150 hours and a
    standard deviation of 450 hours. What should the manufacturer advertise as
    the life of the calculators so that 90% of the calculators are covered?
    A) 2555
    B) 1947
    C) 1410
    D) 1745
    E) 1574
          Answer:

25. Find two values symmetric around a mean of 20 such that they include an
    area equal to 0.75. (standard deviation = 5).
    A) 16.65, 23.35
    B) 19.25, 20.75
    C) 16.25, 23.75
    D) 14.25, 25.75
    E) none of the above
        Answer:

26. The contents of a particular bottle of shampoo marked as 150 ml are found
    to be 154 ml at an average, with a standard deviation of 2.5 ml. What
    proportion of shampoo bottles contain less than the marked quantity?
    Assume a normal distribution.
    A) 0.2192
    B) 0.1096
    C) 0.4452
    D) 0.0548
    E) none of the above
        Answer:

27. The IQ’s of the employees of a company are normally distributed, with a
    mean of 127 and a standard deviation of 11. What is the probability that the
    IQ of an employee selected at random will be between 120 and 130?
    A) 0.2389
    B) 0.3453



Business Statistics                   -6-                    Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                    OCTOBER 1999



    C) 0.1064
    D) 0.1325
    E) 0.4638
        Answer:

28. The GMAT scores of students in a college are normally distributed with a
    mean of 520 and a standard deviation of 41. What proportion of students
    have a score higher than 600?
    A) 0.9744
    B) 0.2372
    C) 0.4774
    D) 0.0256
    E) none of the above
        Answer:

29. If X is a normal random variable with mean 12 and standard deviation 2,
    then the probability that X will exceed 16 is?
    A) 0.04772
    B) 0.0228
    C) 0.9772
    D) 0
    E) 1
         Answer:

30. The sample standard deviation, s, is a point estimate for .
    A) True
    B) False
        Answer:

31. A sample size of 30 or more values is large enough for the Central Limit
    Theorem to be effective.
    A) True
    B) False
          Answer:
32. The Central Limit Theorem states that as the sample size increases, the
    distribution of the sample mean approaches a normal distribution with mean
    equal to the population mean and standard deviation equal to the population
    standard deviation.
    A) True
    B) False
          Answer:

33. In which of the following situations is the Central Limit Theorem not




Business Statistics                    -7-                     Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                   OCTOBER 1999



    appropriate?
    A) When the sample is small and the population is normal.
    B) When the sample is large and the population is normal.
    C) When the sample is large, above 30, and the population is not normal.
    D) When the sample is small, below 30, and the population is not normal.
    E) none of the above
        Answer:

34. The standard deviation of the average number of cassettes a college
    student owns is 14. What minimum sample size of students will give a
    sample standard deviation of at most 4?
    A) 12
    B) 4
    C) 13
    D) 3
    E) 18
        Answer:

35. The average telephone bill in a locality is $70, with a standard deviation of
    $40. In a sample of 50 randomly selected phone connections, what is the
    probability that the sample average will exceed $75?
    A) 0.3106
    B) 0.8694
    C) 0.1894
    D) 0.4483
    E) none of the above
        Answer:

36. Which of the following statements does not refer to the Central Limit
    Theorem?
    A) The expected value of the mean of the distribution of sample means is .
    B) The distribution of sample means is approximately normally distributed.
    C) The standard deviation of the distribution of sample means is equal to .
    D) The Central Limit Theorem is true for any distribution, when the sample
       size is at least 30.
    E) When a non-normal population is sampled, the distribution of sample
       means is still normally distributed, as long as the sample size is large.
        Answer:

37. One way to get a narrower confidence interval, is to increase the sample
    size.
    A) True
    B) False




Business Statistics                   -8-                     Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                      OCTOBER 1999



         Answer:

38. The closer it is necessary for the sample estimate to be to the unknown
    population parameter, the smaller the sample size required.
    A) True
    B) False
        Answer:

39. A type II error is the error that is committed if the null hypothesis is rejected
    when in fact it is true.
    A) True
    B) False
         Answer:

40. When the null hypothesis is not rejected, then we can assume that the null
    hypothesis is certainly true.
    A) True
    B) False
        Answer:

41. The p-value of a hypothesis test is always less than alpha.
    A) True
    B) False
        Answer:

42. The p-value is the chance that you are taking of making a type I error.
    A) True
    B) False
        Answer:

43. The mean annual sales of a company in 36 of its sales offices over the
    country is $23,860,000, with a standard deviation of $2,150,000. A manager
    quotes the annual sales of the company to be $25,000,000. Compute the p-
    value to test whether the sample data provide evidence to reject the
    executive’s claim that the average annual sales are $25,000,000.
    A) 0.2726
    B) 0.3637
    C) 0
    D) 0.0007
    E) 0.0014
        Answer:

44. I would like to test the null hypothesis that the population mean is 50 versus
    the alternative that it is not 50. My sample size is 6, and the sample mean is



Business Statistics                     -9-                      Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                       OCTOBER 1999



    38 with sample standard deviation of 16. At  = 0.05, I should:
    A) strongly reject the null hypothesis
    B) mildly reject the null hypothesis
    C) fail to reject the null hypothesis
    D) accept the alternative hypothesis
    E) there is insufficient information to determine
        Answer:

45. The proportion of defective items is not allowed to be over 15%. A buyer
    wants to test whether the proportion of defectives exceeds the allowable
    limit. The buyer takes a random sample of 100 items and finds that 19 are
    defective. State the null and alternative hypotheses for this test.
    A) H0: p  .15, H1: p > .15
    B) H0: p < .15, H1: p  .15
    C) H0: p = .15, H1: p  .15
    D) H0: p < .15, H1: p > .15
    E) none of the above
          Answer:

46. A manufacturer claims that his tires last at least 40,000 miles. A test on 25
    tires reveals that the mean life of a tire is 39,750 miles, with a standard
    deviation of 387 miles. Compute the test statistic.
    A) t = -0.65
    B) t = 3.23
    C) t = -3.23
    D) t = 0.65
    E) none of the above
         Answer:

47. Given a p-value of 0.065, and using the customary  = 5%, the conclusion
    should be:
    A) accept the null hypothesis
    B) reject the null hypothesis
    C) not enough information to determine
        Answer:

48. A random sample of 36 items gave a sample mean of 48 and a sample
    standard deviation of 12. Compute the p-value to test whether or not the
    population mean is equal to 50.
    A) 0.3413
    B) -0.4772
    C) 0.1587
    D) 0.6826




Business Statistics                    - 10 -                  Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                   OCTOBER 1999



    E) 0.3174
        Answer:

49. I want to conduct a statistical test of whether or not the population mean is
    70. My sample mean is 71, my sample standard deviation is 5, and my
    sample size is 100. The result is:
    A) not significant
    B) significant
    C) very significant
    D) can’t tell
        Answer:


                                GOOD LUCK !




Business Statistics                   - 11 -                   Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                  OCTOBER 1999



                                 FINAL EXAMINATION

                                                        Time:
                                                        9:20 AM – 11:55 AM
                BUSINESS STATISTICS

 Lecturer               Student ID:                     Date:

                        Name:
                                                        November 25, 1999
 Dr. Ho Thanh Phong


Instructions:

d. Every question has the same score.
e. For True/False question, a plus for right answer and minus for wrong answer
f. Discussion is strictly prohibited.




                                Questions
1. The only assumption required for the paired-difference test is that the
   population of differences is normally distributed.
   a) True
   b) False
2. When using the t distribution to test for a difference between two population
   means taken from independent samples the degrees of freedom are: n 1 + n2
   – 2.
   a) True
   b) False
3. The F distribution is the ratio of two chi-square random variables that are
   independent.
   a) True
   b) False
4. If the difference between two sample means is significant, then this is
   evidence that the two samples come from populations with equal means.
   a) True
   b) False




Business Statistics                   - 12 -                  Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                      OCTOBER 1999



5. When testing for the equality of two population means, using  = 0.05 with
   n1 = 12 and n2 =10, the critical points are:
   a) +2.704 and –2.704
   b) +1.96 and –1.96
   c) +2.086 and –2.086
   d) +1.645 and –1.645
   e) none of the above


Use the following to answer questions 6, 7, 8:
A company made a major change in its advertising theme this year and is
interested in knowing whether there is any significant increase in sales over last
year. The following data is the sales in thousands for different stores over the
country, and has been adjusted for inflation. Take the difference as (current
year’s sales – last year’s sales).

                      Store   Last Year’s Sales     Current Year’s
                                                        Sales
                       1             183                 206
                       2             406                 528
                       3             388                 678
                       4             694                 601
                       5             274                 258
                       6             137                 170
                       7              33                 31
                       8            1423                1468
6. State the null and alternative hypotheses to test the hypothesis that the
   change in advertising has increased sales.
   a) H0: D > 0, H1: D  0
   b) H0: D  0, H1: D > 0
   c) H0: D  0, H1: D < 0
   d) H0: D = 0, H1: D > 0
   e) none of the above
7. Find the critical value to test the hypothesis that the change in advertising
   has increased sales, using  = 0.05.
   a) +1.645
   b) +1.96
   c) +2.365
   d) +1.895
   e) none of the above
8. Construct a 95% confidence interval for the average change in sales.
   a) 50.25  (2.365) (40.385)



Business Statistics                        - 13 -               Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                      OCTOBER 1999



    b)   50.25  (1.96) (40.385)
    c)   50.25  (1.895) (40.385)
    d)   50.25  (2.306) (40.385)
    e)   none of the above
Use the following to answer questions 9, 10:
A programmer has written a software package that points out errors in
programs. Previously, this was done manually. The mean number of errors the
software picket out of 100 different programs was 15, with a standard deviation
of 8.2. The mean number of errors picked out manually, out of 100 programs,
was 13, with a standard deviation of 4.9. We want to test whether there is
evidence that this software picks out more errors than checking manually does.
Assume that the software is population 1 and manual checking is population 2.
9. State the null and alternative hypotheses to test whether this software does
   pick out more errors.
   a) H0: 1 - 2  0, H1: 1 - 2 > 0
   b) H0: 1 - 2 = 0, H1: 1 - 2  0
   c) H0: 1 - 2  0, H1: 1 - 2 < 0
   d) H0: 1 - 2 > 0, H1: 1 - 2  0
   e) none of the above
10. Find the critical points to test whether this software does find more errors, at
     = 0.05.
    a) +1.96
    b) +1.645
    c) +1.282
    d) +2.575
    e) +2.33
11. When testing for the equality of two population proportions, the F distribution
    is:
    a) sometimes appropriate
    b) never appropriate
    c) only appropriate if both sample sizes are less than 30
    d) only appropriate if at least one sample is at least 30
    e) used when the two variances are not equal
12. Calculate the pooled variance for the following sample data.

      Sample          Sample Variance            Sample Size
      mean
          40                  10                     12
          30                  12                     15
    a) 3.33




Business Statistics                     - 14 -                   Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                     OCTOBER 1999



    b)   124.64
    c)   11.12
    d)   34.4
    e)   none of the above
13. Compute the p-value for a two-tailed test of the difference in two means,
    with both sample sizes at least 30, if the test statistic is z = 2.50.
    P-value: .....................
14. A survey was conducted to see if the proportion of men and women liking
    this brand of jeans differed. In a sample of 100 men and 90 women, 62 of
    the men liked the jeans, and 66 of the women liked the jeans. Construct a
    95% confidence interval for the difference in the proportion of men and
    women liking these jeans.
    CI = [           ,              ]
15. In fifty different localities, the cable company gives free access to all cable
    channels for a weekend, as a promotional gesture. The mean proportion of
    customers who had the premium channels before the promotion was 20%.
    The mean proportion of customers who had the premium channels after the
    promotion was 26%. The increase significant at a = 0.05.
    a) True
    b) False
16. Your company is interested in a new method of advertising. In order to test
    the new method they have selected thirty-one control and thirty one
    experimental markets. Mean sales in the control markets were 134, 630 with
    a standard deviation of 5,290. Mean sales in the experimental markets were
    138,780 with a standard deviation of 5,730. At the 95% confidence level you
    conclude that the new method is better than the old.
    a) True
    b) False
17. In an ANOVA, if the sum of squares for error is 400, the sum of squares for
    treatment is 180, and the total sample size for the four groups compared is
    88, then the null hypothesis should not be rejected.
    a) True
    b) False
18. In an ANOVA, if: n = 130, r = 3 groups, SSE = 12490, SSTR = 13000, and
    using  = 0.05, the decision should be to reject the null hypothesis.
    a) True
    b) False
19. In ANOVA, the sample size is 500 and seven groups are compared. The
    total sum of squares is 10,000. The decision should be:
    a) do not reject the null hypothesis




Business Statistics                    - 15 -                   Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                    OCTOBER 1999



    b)   reject the null hypothesis immediately
    c)   not enough information given to make a decision on the null hypothesis
    d)   mildly reject the null hypothesis
    e)   decide that the test must be repeated since only seven groups were
         involved
20. In ANOVA, if the sample standard deviation within all four groups under
    study are approximately equal, we should:
    a) immediately decide not to reject the null hypothesis
    b) immediately reject the null hypothesis
    c) mildly reject the null hypothesis
    d) redo the test, since the standard deviation are equal
    e) there is not enough information to make a decision on whether to reject
       or not reject the null hypothesis
21. Analysis of variance is a statistical method of comparing the __________ of
    several populations.
    a) standard deviations
    b) variances
    c) means
    d) proportions
    e) none of the above
22. If the r population means are equal, then MSTR/MSE will be:
    a) more than 1.00
    b) very close to 1.00
    c) very close to 0.00
    d) close to –1.00
    e) a negative value between 0 and –1
Use the following to answer questions 23, 24:
A watch manufacturer markets a particular model with three different straps:
gold, silver and leather. The average number of sales in a week of each watch
are 12, 15 and 11, respectively. An ANOVA to find whether or not the
customers prefer any particular strap over the random sample, shows SSE =
1490 and SSTR = 760.
23. Compute the F test statistic for this hypothesis test.
    a) 0.112
    b) 8.926
    c) 1.96
    d) 9.69
    e) none of the above
24. Write the null hypothesis for this test.
    a) H0: not all the population means are equal
    b) H0: at least one of the population means is not equal to the others




Business Statistics                     - 16 -                 Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                   OCTOBER 1999



     c) H0: 1 = 2 = 3
     d) H0: 1 - 2 - 3  0
     e) none of the above
Use the following to answer questions 25, 26:
A survey is conducted to find whether students like a particular type of music
more than another: rock, pop, classical and jazz. Ratings for each class of
music are collected from 50 students. SSTR = 28,590 and SST = 40,220.
25. Write the null hypothesis to test whether students like these types of music
    equally, or whether there is a preference.
    a) H0: 1 = 2 = 3 = 4
    b) H0: 1 - 2 - 3 - 4  0
    c) H0: s1 = s2 = s3 = s4
    d) H0: at least one of the population means is different
    e) none of the above
26. How many degrees of freedom does the sum of squares for treatments
    have?
    a) 4
    b) 3
    c) 0
    d) 49
    e) 46
Use the following to answer questions 27, 28, 29:
A marketing manager wants to determine if the average advertising spending
per month of his competitors are equal or not. Data over the last six months
reveals the following figures (in thousands of dollars):
A:      11, 17, 27, 35, 43, 38
B:      9, 12, 27, 45, 54, 32
C:      12, 23, 28, 27, 39, 41
27. Compute SSTR for these observations.
    a) 4
    b) 8
    c) 2934
    d) 16
    e) none of the above
28. Calculate the F ration for the ANOVA on these observations.
    a) 0.05
    b) 3.68
    c) 0.02
    d) 0.01
    e) none of the above




Business Statistics                   - 17 -                  Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                   OCTOBER 1999



29. Find the F-value from the table to test the hypothesis that there is no
    difference in average spending among these three companies at  = 0.05.
    a) 3.68
    b) 19.43
    c) 0.02
    d) 3.29
    e) none of the above
Use the following to answer questions 30, 31:
Standardized stock price indicators in three different countries over a week are
listed below. An analyst is interested in knowing if the stock markets of these
three countries are dependent on one another. The ANOVA table is given.
I       II      III
890     900     905
899     900     900
900     887     896
905     906     928
871     893     899
910     900     934
ANOVA table
      Source of       Sum of      Degrees of         Mean
                                                                  F Ratio
      Variation       Squares      Freedom          Square
      Treatment         748
      Error
      Total            3274
30. What are the degrees of freedom for the sum of squares error?
    a) 2
    b) 15
    c) 17
    d) 19
    e) none of the above
31. Find the T value, from the table, for the Tukey test, to determine whether or
not each of the pairs of means are equal. Use  = 0.05.
    a) 3.61
    b) 11.0
    c) 1.96
    d) 3.67
    e) none of the above
Use the following to answer questions 32, 33, 34:
The management of an organization wants to test to see whether the rate of
turnover of employees is the same in all the departments. Samples over the last




Business Statistics                   - 18 -                   Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                      OCTOBER 1999



year show the following as the number of employees having left the company:
Production: 5, 6, 3, 4, 6, 6
Marketing: 3, 4, 4, 4, 3, 5
Finance:    3, 3, 3, 2, 4, 5
Accounting: 2, 3, 3, 5, 6, 4
The ANOVA table is show below:
    Source of         Sum of       Degrees of
                                                   Mean Square        F Ratio
    Variation         Squares       Freedom
    Treatment
    Error              27.00
    Total              36.00
32. State the null hypothesis for this ANOVA.
    a) H0: 1 - 2 - 3  0
    b) H0: all of the population means are different
    c) H0: at least one of the population means is different
    d) H0: 1 = 2 = 3
    e) none of the above
33. If the p-value for this ANOVA is 0.117, what is the conclusion, testing at  =
0.05?
    a) reject the null hypothesis
    b) do not reject the null hypothesis
    c) not enough information to make a decision
    d) at least one of the population means is significantly different
    e) none of the above
34. Construct a 95% confidence interval on the population mean of the Finance
    department.
    a) 3.333  (1.725)(1.162/6)
    b) 3.333  (2.571)(1.162/2.449)
    c) 3.333  (1.725)(1.162/2.449)
    d) 3.333  (2.086)(1.162/2.449)
    e) none of the above
35. In regression analysis, every time that an insignificant and unimportant
    variable is added to the regression model, the R2 decreases.
    a) True
    b) False
36. In multiple regression there is no need to consider the F-test, only the t-tests
    are important.
    a) True
    b) False




Business Statistics                     - 19 -                   Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                    OCTOBER 1999



37. Using multiple regression to regress five independent variables to predict y
    will give the same result as five separate regressions of y versus each
    independent variable.
    a) True
    b) False
38. If H0: 1 = 2 = 3 … = k = 0 is rejected, then we can conclude that there is
    no linear relationship between y and any of the k independent variables in
    the model.
    a) True
    b) False
39. The Mean Square Error, or MSE, is a biased estimator for the variance of
    the population of errors, , denoted by 2.
    a) True
    b) False
40. The square root of the MSE is the standard error of the estimate.
    a) True
    b) False
41. The adjusted multiple coefficient of determination always increases as new
    variables are added to the model, just as R2 does.
    a) True
    b) False
42. When the adjust coefficient of determination decreases when a term is
    included in the multiple regression model, then that term should be retained
    in the model.
    a) True
    b) False
43. In a multiple regression analysis with n = 15 and k = 14, the computer
    reports R2 = 0.9999.
    a) this is an excellent regression
    b) this is a very good regression
    c) this is an average regression
    d) this is not a good regression
    e) not enough information to determine
44. In a multiple regression analysis, MSE = 20, n = 54, k = 3 and SST (total) =
    2000. What is the R2 of the regression?
    a) 0.0
    b) 0.01
    c) 0.99
    d) 1.00
    e) 0.50




Business Statistics                    - 20 -                  Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                             OCTOBER 1999



Use the following to answer questions 45, 46, 47:
The following data gives the monthly sales (in thousands of dollars) for different
advertising expenditures (also in thousands of dollars) and sales commission
percentages.
Sales       245       138   352     322     228       275    560     366
Advertising 16.5      18    22.3    17.4    19        20     32      18.6
Commission 10.5       2     4       3.5     4.5       1.8    9       8.5
Minitab gives the following output from a multiple regression analysis:
Predictor       Coef        Stdev           t-ratio          p
Constant        -138.4      119.0           -1.16            0.297
Advertising     18.742              5.749             3.26           0.022
Commission      11.648              8.420             1.38           0.225
S = 72.88       R1 = 75.7% R-2 (adjusted) = 66.0%
45. What amount of sales would this model predict for advertising expenditures
    of 25,000 and sales commission of 8%?
    a) 42,333
    b) 30,273.6
    c) 561,734
    d) 72,880
    e) none of the above
46. Write the null and alternative hypotheses to test whether or not advertising
    expenditures and sales commission can be used to predict sales.
    a) H0: 1 = 2 = 0; H1: at least one coefficient is not zero
    b) H0: 1  2; H1: 1 = 2
    c) H0: 1 and 2 are not equal to zero; H1: 1 = 2 = 0
    d) H0: 1  2; H1: 1 < 2
    e) none of the above
47. At the 5% level of significance, is either advertising expenditure of sales
    commission percentage or both significant?
    a) only advertising expenditures
    b) both are significant
    c) only sales commission percentage
    d) neither are significant
    e) insufficient information to determine
Use the following to answer questions 48, 49, 50:
Eight students are selected randomly and their present graduate GPA is
compared their undergraduate GPA and scores on standardized tests.
The data are show below:
Present GPA 3.89 3.03 3.34          3.85    3.93      3.06   3.69    3.91




Business Statistics                    - 21 -                         Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                                 OCTOBER 1999



Undergr GPA            3.77   2.75   3.11    3.75     4.00    2.92       3.70    3.88
Std. Scores 700        460    550    690     720      420     670        670
The Minitab regression analysis follows:
Predictor              Coef          Stdev         t-ratio               p
Constant               1.1066                0.2059                      5.37
       0.003
Undergr GPA                   0.4775                  0.1630                     2.93
       0.033
Std. Scores            0.0013392     0.0006693        2.000              .102
Analysis of Variance
 Source               DF         SS              MS                  F                  p
 Regression            2      1.02751
 Error                 5
 Total                 7      1.04255
48. Write the regression equation, letting undergraduate GPA be variable 1 and
    standard scores be variable 2.
    a) y = 0.4775 x1 + 0.0013392x2
    b) y = 0.2059 + 0.1630x1 + 0.0006693x2
    c) none of the others is correct
    d) y = 1.1066 + 0.4775x1 + 0.0013392x2
    e) not enough information given
49. Compute R2.
    a) 99.4%
    b) 98.6%
    c) 20.8%
    d) very close to 100%
    e) insufficient information to determine
50. What is the relationship between R2 and the adjusted R2 for this regression
    model?
    a) both are exactly the same
    b) the adjusted R2 is larger than R2
    c) the adjusted R2 is smaller than R2
    d) both are very small
    e) none of the above
51. A random walk is the difference between successive values of the error
    term.
    a) True
    b) False
52. Prediction and forecasting are the same thing in statistical analysis.




Business Statistics                     - 22 -                            Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                    OCTOBER 1999



    a) True
    b) False
53. Sales of air conditioners follow a seasonal variation.
    c) True
    d) False
54. The ratio-moving-average procedure can be used to deseasonalize data.
    e) True
    f) False
55. The following data is the total units of electricity produced in a country
    annually.
1981 1882 1983 1984 1985 1986 1987 1988 1989
175 179 203 222 225 259 282 292 301
Recode the years so that the average of the years is zero. Compute the slope
  of the trend line.
    a)   237.6
    b)   17.3
    c)   1038
    d)   0.0578
    e)   none of the above
56. Calculate a three-day moving average for the price of stock, for Tuesday
    through Thursday.
      Day               Price
      Monday            50.00
      Tuesday           52.00
      Wednesday         54.00
      Thursday          54.50
      Friday            60.00
     a) 53.50
     b) 54.10
     c) 90.17
     d) 54.00
     e) none of the above
57. The data given below are quarterly sales for a large computer firm, in
    $100,000’s.
     Quarter           Sales
     1991-1            105
     1991-2            110
     1991-3            122
     1991-4            120
     1992-1            125



Business Statistics                     - 23 -                 Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                        OCTOBER 1999



      1992-2            135
Compute the four-quarter moving average for the first four quarters and center it
at the third quarter.
     a) 114.25
     b) 119.25
     c) 116.75
     d) 119.50
     e) none of the above
58. The following are stock prices for a given group of stocks on the Dow Jones.
    Compute the forecast for day 3 using the exponential smoothing method,
    with w = .4.
     Day           Original Dow Jones
                   series
     1                        800
     2                        825
     3                        814
     4                        820
     5                        832
     6                        830
    a) 800
    b) 810
    c) 814
    d) 815
    e) none of the above
59. The average credit bill of the customers of a particular organization have
    been as follows over the last few years:
    1980      117
    1981      193
    1982      318
    1983      367
    1984      397
    1985      456
    1986      525
    1987      591
    1988      653
Estimate a linear trend line for this data. Use this trend line to predict credit
balances of customers for the year 1989.
    a) 698.22
    b) 401.89
    c) 320.08
    d) 721.97
    e) none of the above




Business Statistics                      - 24 -                    Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                      OCTOBER 1999



60. A pattern in a times series model that occurs over more than a year is called
    a _____________ variation.
61. The sign test assumes that the pairs of values are independent.
    a) True
    b) False
62. The sign test can be used to test whether or not the population median is
    equal to some hypothesized value.
    a) True
    b) False
63. The following sequence contains exactly seven runs.
    SSESEESSSESSSE
    a) True
    b) False
64. The Mann-Whitney U test and the rank sum test are the same.
    a) True
    b) False
65. The null hypothesis for the Wilcoxon Signed-Rank Test is that the median
    difference between two populations is zero.
    a) True
    b) False
66. You are testing for independence using the chi-square distribution. The
    contingency table has two rows and four columns. The computed value of
    chi-square is 6.5. The p-value is:
    a) less than 0.005
    b) between 0.005 and 0.01
    c) between 0.01 and 0.05
    d) between 0.05 and 0.10
    e) greater than 0.10
Use the following to answer questions 67, 68:
The size of the operating system of a microcomputer (in Kilobytes) has been
varying as shown below, over the last eight years.
38, 41, 45, 43, 44, 42, 47, 50
67. State the null hypothesis that will test for the existence of a positive trend in
    this data.
    a) H0: p(+)  0.5
    b) H0: p(+)  0.5
    c) H0: p(+)  0.5
    d) H0: p(+) > 0.5
    e) H0: p(+) < 0.5




Business Statistics                     - 25 -                    Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                                     OCTOBER 1999



68. Compute the test statistic to test for a positive trend.
    a) T = 2
    b) T = 3
    c) T = 4
    d) T = 8
    e) T = 6
69. A computer random number generator gives the following random numbers:
    5 8     5 6        9 8     7    6    6    4    3    1        1   1     0        1   1    1        0
    2
    How many runs are in this data?
    a) 20
    b) 12
    c) 11
    d) 19
    e) none of the above
70. The management of a museum wants to know if the proportions of three age
    groups of visitors, those under 18, those between 18 and 50, and those over
    50, who buy souvenirs from the gift shop are equal. Over a particular week,
    the following number of people enter the museum:

                             Visitors         Number who                  Totals
                                                 buy
    Under 18                  108                 61                       169
    18 – 50                   137                 93                       230
    Over 50                   81                  49                       130
    Totals                    326                203                       529
Compute the chi-square value to test whether the proportion of visitors buying
from the museum gift shop is the same in all the age groups.
    a) 0.5
    b) 0.15
    c) 0.8927
    d) 5.2
    e) none of the above

Use the following to answer questions 71, 72:
A manager compares the profits made by two products over the last year. The
following table gives the data in thousands of dollars.

Month     1           2      3      4        5     6        7        8         9        10       11       12
A         23          28     55     47       22    19       15       26        37       32       46       53
B         34          27     44     56       52    43       49       34        27       41       48       39




Business Statistics                           - 26 -                           Dr. Ho Thanh Phong
SAV 6 - PROGRAM                                                     OCTOBER 1999



71. Use the Mann-Whitney U test to determine whether or not there is statistical
    evidence that the profits over one product are greater than the profits made
    from the other product. Give the U statistic. Assume that A is sample 1.
    a) 124.5
    b) 97.5
    c) 175.5
    d) 751.5
    e) none of the above
72. Compute the E (U) for the Mann-Whitney U statistic for this data.
    a) 72
    b) 24
    c) 144
    d) 66
    e) none of the above
73. The only assumptions required for the Mann-Whitney U test are:
    a) independent samples
    b) random samples
    c) normal populations
    d) a and b
    e) a, b and c
74. The following data gives the returns on two securities, A and B, over a
    period of 12 months.
Month     1           2    3    4    5     6     7      8      9        10   11     12
A         17          18   16   17   18    19    19     15     16       15   17     16
B         14          16   18   19   17    16    15     18     13       14   15     12
Compute the test statistic, for the Wilcoxon signed-rank test to determine
whether or not there is a difference in the returns of the two securities.
   a) 17.5
   b) 37.5
   c) 12
   d) 8.5
   e) none of the above
75. The average life of a battery is supposed to be 250 hours of continuous
    operation. A random sample of 25 batteries is subject to discharge and the
    lifetime is recorded. The data is as follows (in hours):
    214, 289, 263, 291, 240, 207, 277, 252, 285, 287, 250, 297, 268, 286, 211,
    232, 282, 216, 223, 234, 219, 280, 239, 249, 230.
    Using the sign test to test whether there is statistical evidence to conclude
    that the life of the battery is less than 250 hours, find the test statistic.
    a) 10




Business Statistics                   - 27 -                   Dr. Ho Thanh Phong
SAV 6 - PROGRAM                               OCTOBER 1999



    b)   12
    c)   13
    d)   25
    e)   none of the above




                             GOOD LUCK !




Business Statistics              - 28 -    Dr. Ho Thanh Phong

								
To top