1. A study compares the effectiveness of two methods for training new salespeople. The situation could be described as follows: The company selects 22 sales trainees who are randomly divided into two...

1.
A study compares the effectiveness of two methods for training new salespeople. The situation could be described as follows: The company selects 22 sales trainees who are randomly divided into two experimental groups—one receives type
A
and the other type
B
training. The salespeople are then assigned and managed without regard to the training they have received. At the year’s end, the manager reviews the performances of salespeople in these groups and finds the following results:

A
Group Average Weekly Sales $1,500
Standard Deviation 225

B
Group $1,300 251

1. Set up the null and alternative hypotheses needed to attempt to establish that type
   A
   training results in higher mean weekly sales than does type
   B
   training.


2. Because different sales trainees are assigned to the two experimental groups, it is reasonable to believe that the two samples are independent. If the normality assumption holds, and using the equal variances procedure, test the hypotheses you set up in part
   a
   at levels of significance 0.05 and 0.001. How much evidence is there that type
   A
   training produces results that are superior to those of type
   B?


3. 
   Use the equal variances procedure to calculate a 95 percent confidence interval for the difference between the mean weekly sales obtained when type
   A
   training is used and the mean weekly sales obtained when type
   B
   training is used. Interpret this interval.
   
   

3.
A marketing research firm wishes to compare the prices charged by two supermarket chains (M and A.) The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 M’s stores are $121.92 and $1.40, respectively. It is also found that the mean and the standard deviation of the shopping expenses at the 10 A’s stores are $114.81 and $1.84, respectively. Assuming normality, test to see if the corresponding population variances differ by setting alpha equal to .05. Is it reasonable to use the equal variances procedure to compare population means? Explain.

5.
The loan officers at a large bank can use three different methods for evaluating loan applications. Loan decisions can be based on (1) the applicant balance sheet (B), (2) examination of key financial ratios (F), or (3) use of a new decision support system
(D). To compare these three methods, four of the bank’s loan officers are randomly selected. Each officer employs each of the evaluation methods for one month (the methods are employed in randomly selected orders). After a year has passed, the percentage of bad loans for each loan officer and evaluation method is determined. The data obtained by using this randomized block design are given in the table below. Completely analyze the data using randomized block ANOVA.



6.
In the book
Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil A. Firtle discuss the relationship between delivery time and computer- assisted ordering. A sample of 40 firms shows that 16 use computer-assisted ordering, while 24 do not. Furthermore, past data are used to categorize each firm's delivery times as below the industry average, equal to the industry average, or above the industry average. The results obtained are given in the following table.

1. Test the hypothesis that delivery time performance is independent of whether computer-assisted ordering is used. What do you conclude by setting
   a
   = .05? ?


2. Verify that a chi-square test is appropriate. ?


3. Is there a difference between delivery-time performance between firms using ?computer-assisted ordering and those not using computer-assisted ordering? ?


4. Carry out graphical analysis to investigate the relationship between delivery-time ?performance and computer-assisted ordering. Describe the relationship. ?