1. A bank with a branch located in a commercial district of a city has developed an improved process for serving customers during the noon to 1 P.M. lunch period. The waiting time (operationally defined as the time elapsed from when the customer enters the line until he or she reaches the teller window) of all customers during this hour is recorded over a period of one week. A random sample of 15 customers is selected, and the results (in minutes) are as follows:

4, 5, 3, 5.2, 3.6, 4.8, 5, 3.7, 6, 3.2, 4.5, 4.7, 5.14, 6.14, 3.86

Suppose that another branch located in a residential area is also concerned with the noon to 1 P.M. lunch period. Another set of random sample of 15 customers is also selected, and the results (in minutes) are as follows:

4.7, 5.5, 3.8, 4.2, 3.6, 4.8, 5, 3.7, 6.3, 3.4, 4.6, 4.3, 6.14, 5.16, 3.96

We can assume that the population variances are equal and use significance level of 0.05 to conduct a test to see if the mean waiting time in the banks located in commercial districts is significantly different from the mean waiting time in the banks located in residential areas.

2. A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below. The buyer believes that the prices are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01. Please use the appropriate test to see if there is evidence that his primary supplier is overcharging.

    Primary Material Supplier     Secondary Supplier

1                         $55                             $45

2                         $48                             $47

3                         $31                             $32

4                         $83                             $77

5                         $37                             $37

6                         $55                             $54

7                         $40                             $ 42

8                         $78                             $ 75

9                         $65                             $ 63

10                       $34                             $40

3. An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the average, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is given below. Please use the appropriate test to see if there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same. Level of significance is assumed to be 0.01.

Package 1: 12, 14, 9, 11, 16

Package 2: 2, 4, 7, 3, 1

Package 3: 10, 9, 6, 10, 12

Package 4: 7, 6, 6, 15, 12

4. 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. These data are presented in the table that follows.

Broker Clients Sales

1             48         72

2             11         37

3             42         64

4             33         55

5             15         29

6             15         34

7             25         58

8             36         59

9             28         44

10           30         48

11           17         31

12           22         38

Please use Excel to conduct the Simple Linear Regression Analysis on the data set above and show the summary output. Please attach the output. 

Please use the regression analysis results you get from the information above to answer the following questions. Confidence level is 95%.

Please write down the regression equation.

The individual value prediction for the amount of sales (in $1,000s) for a person who brings 25 new clients into the firm is ________.Please show your calculation.

What is the total variation of “Sales”?

What is the variation of “Sales” that can be explained by the regression equation?

What is the variation of “Sales” that cannot be explained by the regression equation?

What percentage of the variation in “Sales” is explained by its regression on “number of new clients”?

What is the coefficient of determination?

What is the standard error of estimate?

Is there a significant relationship between the variable “Sales” and the variable “number of new clients” at the 5% significance level? Please explain it. 

What is the calculated value of the t statistic to test the hypothesis for the significance of the coefficient on number of new clients? 

Is the coefficient on number of new clients significantly different from zero? Please explain it.

What does the 95% confidence interval for the slope of the regression line mean?

What is the sum of squares of X (SSx) for these data? Please show your calculation.

Suppose the managers of the brokerage firm want to obtain a 95% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new clients. What is the confidence interval estimate?

Suppose the managers of the brokerage firm want to obtain a 95% prediction interval for the sales made by a broker who has brought into the firm 18 new clients, what is the prediction estimate? 

What are the assumptions of the Simple Linear Regression model?

The relationship between dependent variable and independent variable has to be linear.

Error terms have to be independent of each other.

Error terms have equal variances for all the values of X.

Error terms follow normal distribution.

All of the above are correct.

The simple linear regression uses the least squares method to find the regression coefficients, and the least squares method minimizes which of the following?

SSR

SSE

SST

All of the above