# SM 1.11.4 Exams by ashrafp

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```									SAV 6 - PROGRAM                                                   OCTOBER 1999

MID-TERM EXAMINATION

Time:
9:30 AM – 11:30 AM

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

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

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
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

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

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

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

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:

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

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

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%
13. What percentage of passengers has at least one bag?
A) 60%
B) 30%
C) 10%
D) 90%
E) 40%

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

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
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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

31. A sample size of 30 or more values is large enough for the Central Limit
Theorem to be effective.
A) True
B) False
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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

GOOD LUCK !

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

FINAL EXAMINATION

Time:
9:20 AM – 11:55 AM

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
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
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?
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
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

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