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					                                  Business and Economic Statistics
                                             BAD 2323
                                            Final Exam

Part I            Multiple Choice

1.       A discrete distribution is usually the result of
                 A. a small probability                         C. a small sample
                 B. a measurement                               D. a count

2.       An event is the collection of one or more
                A. experiments                          C. probabilities
                B. combinations                         D. outcomes

3.       The observation of some activity or the act of taking some measurement is called
                 A. an experiment                     C. a probability
                 B. an event                                    D. an outcome

4.       The mean of a discrete probability is also called the
                A. expected value                              C. variance
                B. standard deviation                          D. median

5.       A listing of all possible outcomes of an experiment and the corresponding probability is called:
                   A. the normal rule                          C. a probability distribution
                   B. the complementary rule                   D. a random variable

6.       If A and B are mutually exclusive events then P(A or B) equals
                 A. P(A) + P(B) - P(A and B)                 C. P(A) + P(B)
                 B. P(A) x P(B)                      D. P(A|B) + P(B|A)

7.       If the probability of an event occurring is 0.40, that means
                   A. the event has a 40% chance of not occurring
                   B. the event has a 60% chance of not occurring
                   C. the complement of the event has a 0.40 chance of occurring
                   D. the event has a 30% chance of occurring

8.       Which formula represents the probability of the complement of event A?
                 A. 1 + P(A)                                 C. P(A) - 1
                 B. 1 - P(A)                                 D. P(A)

9.       To construct a probability distribution, we need to know
                 A. only the mean                               C. the size of the sample
                 B. the number of trials and the       D. mean and variance are equal
                      probability of success

10.      The difference between the binomial and the hypergeometric distribution is
                  A. the trials are not independent for the binomial
                  B. the probability of a success is not the same for all trials in the hypergeometric
                  C. binomial requires a large sample
                  D. the mean and standard deviation are the same for the binomial

11.      Which distribution would be most appropriate if one wanted to find the probability of selecting
         four honest politicians (without replacement) from a sample of 25 politicians?
                 A. Hypergeometric                             C. discrete
                 B. Binomial                                   D. Poisson




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                                         Final Exam
12.   If A and B are independent events, then the probability of A and B equals
               A. P(A) + P(B) - P(A and B)                  C. P(A) + P(B)
               B. P(A) x P(B)                      D. P(A|B) + P(B|A)

13.   Two events occurring at the same time is called
             A. prior probability                            C. joint probability
             B. conditional probability                      D. subjective probability

14.   Which of the following is NOT a requirement for a discrete probability distribution?
              A. the sum of the probabilities equal to 1.00
              B. the outcomes are mutually exclusive
              C. the trials are independent
              D. the probability of each outcome is between 0 and 1.00

15.   Which of the following is NOT a requirement for the binomial distribution.
              A. only two outcomes are possible
              B. the probability of a success changes from one trial to the next
              C. the sample size must be fixed
              D. trials must be independent

16.   Which of the following statements is true about a poisson distribution?
              A. the probability of a success is small
              B. the outcome of one trial affects the outcome of another
              C. the sample size is large
              D. the probability changes after each trial
              E. A & C above

17.   The particular result of an experiment is called
               A. an outcome              C. a probability
               B. combinations            D. an experiment


18.   Which of the following statements about probability is always correct?
              A. a probability can range from 0 to 1
              B. a probability close to 0 means the event is likely to happen
              C. a probability close to 1 means the event is NOT likely to happen
              D. all of the above are correct
              E. none of the above are correct

19.   A probability distribution that can assume only certain values within a range is called:
              A. a discrete probability distribution
              B. a continuous probability distribution
              C. a random variable distribution
              D. a Poisson probability distribution

20.   According to the classical definition of probability
              A. all events are equally likely
              B. the probability is based on guesses
              C. the number of success is divided by the number of successes
              D. one outcome is exactly three times the next




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                                             Final Exam
21.       The normal distribution is
                  A. discrete distribution
                  B. continuous distribution
                  C. asymmetric
                  D. all of the above

22.       The correction for continuity is used when
                   A. the distribution is continuous
                   B. the z-scores are less than 0.05
                   C. the distribution is discrete
                   D. the z-scores are integers

23.       A normal distribution is completely described by
                 A. its mean and standard deviation
                 B. its standard deviation
                 C. its mean
                 D. none of the above

24.       Any normal distribution can be converted to a standard normal distribution
                 A. A. by finding =
                 B. by determining that  is greater than 5
                 C. by finding 
                 D. by calculating the z-value

25.       What is the value of the constant e in a Poisson distribution?
                   A. 3.1417         B. 2.678 C. 2.1787           D. 2.71828


      26. In a two sample test of means for independent samples, the equal sign always appears in
               A. The null hypothesis
               B. The alternative hypothesis
               C. The upper tail of the test statistic
               D. None of the above

      27. A random sample of 10 observations is selected from the first normal population and 8 from the
          second normal population. For a one tailed test of hypothesis (.01 significance level) to determine
          if there is a difference in the population means, degrees of freedom are
               A. .18
               B. 16
               C. 17
               D. None of the above

      28. Which of the following is NOT a requirement for the two sample test of means for independent
          samples when both samples contain less than 30 observations?
             A. Equal sample sizes
             B. Normal population
             C. Equal population standard deviations
             D. All of the above are required

      29. In a two sample test of means for independent samples, we use the z distribution when
               A. Both populations are positively skewed
               B. Population standard deviations are equal
               C. Both samples are at least 30
               D. None of the above



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                                       Final Exam
30. Which of the measures of central tendency is the largest in a positively skewed distribution?
       A. Mean
       B. Median
       C. Mode
       D. Cannot tell from the information given

31. A discrete variable is
        A. An example of a qualitative variable
        B. Can assume only whole numbers
        C. Can assume only clearly separated values
        D. Cannot be negative

32. The term ANOVA
        A. Stands for Another Numerical Observation of the Variance
        B. Stands for Analysis of Variance
        C. Has no special meaning
        D. None of the above

33. The term “Treatment” refers to
        A. The variation within the cells
        B. The numerator degrees of freedom
        C. A source of variation
        D. None of the above

34. Which level of measurement is required for the mode?
       A. Nominal
       B. Ordinal
       C. Interval
       D. Ratio

35. In a symmetric distribution
         A. The mean, median, and mode are all equal
         B. The median is the largest measure of location
         C. The mean is the largest measure of location
         D. The standard deviation is the largest value

36. Which of the following is NOT a characteristic of the F distribution?
       A. It is positively skewed
       B. It is based on two sets of degrees of freedom
       C. It cannot be negative
       D. It is a discrete distribution

37. The ratio scale of measurement
        A. Usually involves ranking
        B. Is usually based on counting
        C. Has a meaningful zero point
        D. Cannot assume negative values

38. A disadvantage of the range is
        A. It does not exist for some sets of data
        B. It is in different units from the mean
        C. Only two values are used in its calculation
        D. All of the above




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                                             Final Exam
      39. Which of the following measures of central tendency is affected most by extreme values?
             A. Mean
             B. Median
             C. Mode
             D. Geometric Mean

      40. The standard deviation is
              A. Based on squared deviations from the mean
              B. Is in the same units as the mean
              C. Uses all the observations in its calculation
              D. All of the above
      41. To convert a frequency distribution to a relative frequency distribution
              A. Multiply the class frequency by 100
              B. Divide the lower limit of the first class by the class interval
              C. Divide the class frequency by the number of observations
              D. Find the difference between consecutive lower limits

      42. The general idea of analysis of variance is to compare estimated variances
              A. From both between the treatment means and within the treatment means
              B. Based on several treatments
              C. From within the treatments
              D. None of the above

      43. The ordinal scale of measurement
              A. Has a meaningful zero point
              B. Is based on ranks
              C. Cannot assume negative values
              D. All of the above

44.       For a 2 goodness-of-fit test
          A. There is only one degree of freedom
          B. The rejection region is in the upper right tail
          C. The scale of measurement is interval
          D. We must assume a normal population

45.       For a 2 goodness-of-fit test
          A. There is only one degree of freedom
          B. The rejection region is in the upper right tail
          C. The scale of measurement is interval
          D. We must assume a normal population.

      46. Which of the following is not a characteristic of the 2 distribution?
             A. Its shape is based on the sample size.
             B. It is not negative.
             C. It is positively skewed.
             D. It approaches a normal distribution as the degrees of freedom increase.

      47. To conduct a nonparametric test the
              A. Population must follow the normal distribution.
              B. The standard deviation must be known.
              C. It is not necessary to make any assumption about the shape of the population.
              D. The data must be at least interval scale.




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                                      Final Exam
48. In a contingency table
         A. The number of rows must be the same as the number of columns.
         B. A variable is classified according to two criteria.
         C. There must be at least 10 observations in each cell.
         D. All of the above:

49. In a multiple regression equation there
         A. Are two or more independent variables.
         B. Is only one dependent variable.
         C. Is one intercept value.
         D. All of the above.

50. A scatter diagram is a chart
        E. In which the dependent variable is scaled along the vertical axis.
        A. In which the independent variable is scaled along the horizontal axis.
        B. That portrays the relationship between two variables.
        C. All of the above.

51. In correlation analysis
         A. We consider several independent variables.
         B. We study the strength of the association between two variables.
         C. We consider the intercept with the Y-axis.
         D. None of the above.

52. The sample coefficient of correlation
        A. Has the same sign as the slope, i.e. b.
        B. Can range from –1.00 up to 1.00
        C. Is also called Pearson's r.
        D. All of the above.

53. The standard error of the estimate is
        A. Based on squared deviations from the regression line.
        B. May assume negative values.
        C. Is in squared units of the independent variable.
        D. All of the above.

54. Which of the following is NOT a necessary condition for regression analysis?
       A. The standard deviation of each of the conditional distributions must be the same.
       B. The Y values are independent.
       C. For each X value, there is a group of Y values and these Y values are normally distributed.
       D. The slope of the regression line is positive (increasing).

55. Which of the following is NOT based on squared deviations from the regression line?
       A. The coefficient of correlation.
       B. The coefficient of determination.
       C. The standard deviation.
       D. The standard error of estimate.




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                                            Final Exam




Part II Problems
           1.     A retail trade management journal reported that the typical shopper spends an average of
                  1.80 hours per visit in a shopping mall. A sample of 8 shoppers at the Tupelo Mall
                  revealed the following times. At the 0.01 significance level, can we conclude that
                  shoppers at the Tupelo Mall spend less than a mean of 1.80 hours?

     1.4    1.7     1.6 2.1    1.6 1.9    1.7 1.7

     a. State the Null and Alternative hypothesis




     b. State the decision rule




     c. Compute the value of the test statistic




     d. Compute the p-value




     e. What is your decision regarding the null hypothesis?




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                               Final Exam
2.   As part of a safety check, the Mississippi Highway Patrol randomly stopped 65 trucks
     and checked their tire pressures. The sample mean was 32 pounds per square inch with a
     sample standard deviation of 2 pounds per square inch. Develop a 98% confidence
     interval for the population mean.




3.   A survey is being conducted on the election of a Student Government President. A pilot
     survey has determined the variance of the population to be 0.25. If the poll is to have a
     98% confidence interval and must be within four percentage points, how many people
     should be surveyed?




4.   Be Fast Oil Changers advertises a mean time of 10 minutes for an oil change with a
     standard deviation of 3.0 minutes. What percentage of oil changes is completed? Show
     All work Including graphs.

A. Between 10 and 15 minutes



B. Less than 12 minutes




C. Less than 30 minutes




D. Between 12 and 15 minutes



E. Twenty percent of their jobs take more than how much time?




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                                                   Final Exam
                     5.   According to a recent survey, 70 % of all customers will return to K-Mart. Suppose eight
                          customers are selected at random, what is the probability that :

i.                                A. exactly 5 of the customers will return?



           ii.                    all eight will return?



          iii.                    At least 7 will return?




          iv.                     At least one will return?


           v.                     How many customers would be expected to return to Wal-Mart?




     6.
     Is the following sample Positively Skewed? YES NO
     Explain your answer.

                 6    12      7     12      8      4        5




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                                             Final Exam
                                              Treatment                       Treatment
                                              1              Treatment 2      3
                                                      9                13             10
                                                      7                20               9
                                                     11                14             15
                                                      9                13             14
                                                     12                               15
                                                     10




 Anova: Single Factor

 SUMMARY
        Groups                    Count          Sum           Average         Variance
 Treatment 1                              6            58    9.666666667      3.06666667
 Treatment 2                              4            60             15      11.3333333
 Treatment 3                              5            63           12.6              8.3


 ANOVA
   Source of Variation             SS             df              MS               F            P-value         F crit
 Between Groups                     70.4                2           35.2      5.11793215       0.024704       3.885294
 Within Groups                  82.53333               12    6.877777778

 Total                          152.9333               14



7. Given the above data analysis, List all five steps with appropriate data of the hypothesis test and give
your decision.




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                                             Final Exam


              8. In the Tupelo, Mississippi TV market there are three commercial television stations, each
              with its own evening news program from 6:00 until 6:30 P.M. According to a report in this
              mornings Daily Journal, a random sample of 150 viewers last night revealed 53 watched
              WTVA (Channel 9), 64 watched WLOV (Channel 13), and 33 watched WCBI (Channel 27).
              At the .05 significance level, is there a difference in the viewers watching the three channels?
              Show all five steps.

 TV Station            Frequency
 WTVA                      53
 WLOV                      64
 WCBI                      33




9. There are 400 workers employed at Tom’s, Inc. A sample of 30 workers revealed that
       18 graduated from Northeast Community College. Construct the 99 percent
       confidence interval for the proportion of all workers who graduated from
       Northeast.




10. A recent study of the normal population of American Automobile Dealers Association
revealed the mean amount of profit per car sold of a sample of 20 dealers was $290, with
a standard deviation of $105. Develop a 95 percent confidence interval for the population
mean.




11.     11. A recent study of Northeast students showed that 25% take Spanish, 20% take
        French, and 10% take both. What percent of students take Spanish or French?


12.     The number of claims for missing baggage at the Tupelo airport averages four
        per Month. What is the probability that in a given month, there will be:

                  a.    fewer than 3 claims
                  b.    exactly three claims
                  c.    three or more claims
                  d.    more than three claims


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                                        Final Exam

13. The following data give the daily spending by college students.

271      192     429    205    100     159     321      279     116   363   181      294    279


151      570     90     266    309     240     342

A.    How many classes do you recommend?
B.    What class interval do you recommend?
C.    What is the lower limit of the first class?
D.    Organize the data into a Frequency Distribution
E.    What group or interval has the highest spending habits?


14. The law firm of Yarber and Yarber is located in downtown Doskey Mississippi.
There are 10 partners in the firm; 6 live in Booneville and 4 live in Fulton. The
managing partner wants to appoint a committee of four partners to look into moving the
firm to Tupelo. If the committee is selected at random from the 10 partners, what is the
probability that :
        a. two member live in Booneville and the others live in Fulton?




          b. at least one member lives in Booneville?


15. Based on a recent survey, 90% of all Wal-Mart customers will use the same store
location. If seven customers are selected at random, what is the probability that:

         a. exactly 4 customers will use the same store?

         b. less than 2 will use the same store?

         c. at least one will use the same store?

         d.   How many customers will be expected to use the same store?




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                             Business and Economic Statistics
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                                         Final Exam
16. A recent article in the Wall Street Journal reported that the 30 year mortgage rate is
now less than 6%. A sample of 8 small banks in Mississippi revealed the following 30-
year mortgage rates (in percent).

4.8 5.3       6.5    4.8      6.1       5.8   6.2        5.6

At the .01 significance level, can we conclude that the 30-year mortgage rate for small
banks is less than 6%? Prove your answer using the five step method and estimate the
p-value.

17. The following hypotheses are given:
          Ho: π = .40
          H1: π ≠ .40
A sample of 120 observations revealed that p = .30. At the .05 significance level, can the null hypothesis
be rejected? Use the five step method to solve this problem.


18. The null and alternative hypotheses are:

Ho:       μd ≤ 0
H1:       μd > 0

The following sample information shows the number of defective units produced on the day shift and the
evening shift for a sample of four days last month.

                                                               Day
                                    1                           2           3                     4
Day                    10                           12               15                  16
Evening                8                            9                11                  16

At the .10 significance level, can we conclude there are more defects produced on the evening shift? Show
all five steps. Interpret the results.


19. A sample of 64 observations is selected from a population of men. The sample mean is 2.68 and the
sample standard deviation is 0.75. A sample of 49 observations is selected from a population of women.
The sample mean is 2.58 and the sample standard deviation is 0.65. Conduct the following test of
hypothesis using the .05 significance level.

Ho: µ men ≤ µ women
H1: µ men > µ women

A. Is this a one or two tailed test?

B. State the decision rule.

C. Compute the value of the test statistic.

D. What is your decision regarding the null?




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