# Statistics-QA453

## Statistics-QA453 Online Services

Problem 1

High school students planning to attend university were randomly assigned to watch one of four videos about SMU. Each video differed in the particular aspect of university life of students that was emphasized: athletics, academics, social life, or art and culture. After watching a video, each student was given a questionnaire that measured his or her desire to attend SMU. Student’s answers were analyzed to provide a measure of their desire to attend SMU. Scores reflect the percentage of questions indicating a strong preference to attend SMU (high scores reflect a greater desire to attend SMU). A total of 16 students were shown one of the videos. The data is presented in the table below.

68 89 74 76
56 78 82 71
69 81 79 69
70 77 80 65

a) At the 1% level of significance, do the data suggest that the type of activity emphasized in a university video affect the desire of prospective students to attend SMU? Use the classical approach. (16 pts)

(1) Hypothesis (2 pts)
(2) Test Statistic (3 pts)
(3) Decision Rule (2 pts)
(4) Analysis (6 pts)
(5) Decision/Conclusion (3 pts)
(6) Discuss the underlying assumptions of the test used in (a). (4pts)

Problem 2

A major Canadian bank is interested in comparing three alternative methods that could be used for evaluating loan applications. Loan decisions can be based on

(a) the applicant’s balance sheet (method B),

(b) examination of key financial ratios (method F), or

(c) use of a new decision support system (method D). In order to compare these three methods, four of the bank’s loan officers were randomly selected from among Ontario loan officers. Each officer employed each of the three methods for one month when making loans. The methods were used in different random orders by each of the officers in the study. After two years had passed, the number of bad loans for each loan officer using each of the evaluation method was determined. This data appears in the table below. Loan Officer Loan Evaluation Method

B F D
1 8 5 4
2 6 4 3
3 5 2 1
4 4 1 0

a) Determine if there is a difference among the three methods in the mean number of bad loans made. Use a significance level of 5% and p-value approach. (10 pts)

b) Use Excel to solve the problem in part (a); attach the Excel printout in the space provided below. Do you get the same results as in part (a)? (5 pts)

c) What are the strengths of this type of experimental design? (3 pts)

d) What are the weaknesses of this type of experimental design? (2 pts)

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Problem 3

The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. The data is presented in the table below:

Broker 1 2 3 4 5 6 7 8 9 10 11 12
Clients 27 11 42 33 15 15 25 36 28 30 17 22
Sales 52 37 64 55 29 34 58 59 44 48 31 38

a) Is there a relationship between the numbers of new clients a broker brings and the sales generated by the broker? In order to answer this question you will need to calculate the correlation between the number of new clients and sales. What is the correlation between the number of new clients and sales? If there is a relationship, describe it in your own words. (5 pts)

b) Find the equation of the regression line for predicting a broker’s sale from the number of new clients he brings in. (5 pts)

c) Plot the 12 points in a scatter plot and draw the regression line. (5 pts)

d) Is the sign of the slope logical? If the slope had the opposite sign, what would that tell you? (2 pts)

e) What would you predict for the amount of sales (in \$1,000) for Horatio who brings in 25 new clients into the firm? (3 pts)

f) What is the 95% confidence interval (i.e., prediction interval) for the amount of sales (in \$1,000) for Horatio who brings in 25 new clients into the firm? (5 pts)

g) What is the 95% confidence interval for the mean amount of sales (in \$1,000) for a broker who brings in 25 new clients into the firm? (5 pts)

Product code:Statistics-QA453