# Hypothesis Tests

1. According to a survey conducted in October 2001, consumers were trying to reduce their credit card debt(Extracted from M. Price," Credit Debts Get Cut Down to Size," Newsday, November 25,2001,pF3) . Based on a sample of 1,000 consumers in October 2001 and in October 2000, the mean credit card debit was $2411 in October in October 2001 as compared to $2814 in October 2000.Suppose that the standard deviation was $847.43 in October 2001 and $976 in October 2000.

Assuming that population variances from both years are equal, is there evidence that the mean credit card debt was lower in October 2001 than in October 2000?(use the a=0.05 level of significance

2. A news paper article discussed the opening of a Whole foods market in the Times Warner Building In New York City The following Data (stored in the file ) compared the prices of some kitchen staples at the Whole Foods market and at the Fairway supermarket located about 15 blocks from the time Warner Building:

Items

Whole Foods Fairway

Half-gallon of milk 2.19 1.35

Dozen eggs 2.39 1.69

Tropicana orange juice (64 oz) 2.00 2.49

Head of Boston lettuce 1.98 1.29

Ground Round 1lb 4.99 3.69

Bumble tuna (6oz) 1.79 1.33

Granny Smith Apples (1lb) 1.69 1.49

Box Dececco linguini 1.99 1.59

Salmon Steak, (1Lb) 7.99 5.99

Whole chicken per pound 2.19 1.49

At the 0.01 level of significance, is there evidence that the mean price is higher at whole Foods Markets than at the Fairway supermarkets?

3. A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behaviors. Among the questions asked was, "Do you enjoy shopping for clothing?" Of 240 males, 136 answered yes. Of 260 females, 224 answered yes.

Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing at the 0.01 level of significance?

4. The retailing manager of a supermarket chain wants to determine whether product location has any effect on the sale of pet toys. There different aisle locations are considered: front, middle, and rear. A random sample of 18 stores is selected, with 6 stores randomly assigned to each aisle location. The size of the display area and price of the product are constant for all stores. At the end of a one-month trial period, the sales volumes (in thousands of dollars) of the product in each store were as follows (and are stored in the file).

Aisle locations

Front Middle Rear

8.6 3.2 4.6

7.2 2.4 6.0

5.4 2.0 4.0

6.2 1.4 2.8

5.0 1.8 2.2

4.0 1.6 2.8

At the 0.05 level of significance, is there evidence of a significant difference is mean sales among the various aisle locations?

If appropriate, which aisle locations appear to differ significantly in mean sales?

What should the retail manager conclude? Fully describe the retailing managers options with respect to aisle locations

5. Suppose you heard a rumor that there was a difference in the salaries for men and women at your company. You decide to take a sample of employees and test the claim. Assume the "Cumba" database file represents a random sample of 100 employees.

Using the "Hypothesis Tests Two Sample" file and a .05 significance level, test whether there is a difference in the mean salary for men versus women. Note: Use salary and gender data.

6. Where people turn to for news is different for various age groups. A study indicated where different age groups primarily get their news:

Age group

Media Under 36 36-50- 50+

Local TV 107 119 133

National TV 73 102 127

Radio 75 97 109

Local news paper 52 79 107

Internet 95 83 76

At the 0.05 level of significance, is there evidence of a significant relationship between the age group and where people primarily get their news? If so, explain the relationship.

7. A brokerage house wants to predict the number of trade executions per day, using the number of incoming phone calls as a predictor variable. Data were collected over a period of 35 days and are stored in the file.

Use the least-squares method to complete the regression coefficients b o and b1.

Interpret the meaning of b0 and b1 in this problem.

Predict the number of trades executed for a day in which the number of incoming calls is 2,000.

Should you use the model to predict the number of trades executed for a day in which the number of incoming calls is 5,000? Why or why not?

Determine the coefficient of determination r2, and explain its meaning in this problem.

At a 0.05 level of significance, is there evidence of linear relationship between the volume of trade executions and the number of incoming calls?

Construct a 95%prediction interval estimate of the trades executed for a particular day in which the number of incoming calls is 2,000.

8. Using the "Cumba" database file, create a pivot table of management level versus gender. Then copy the data from the table into a chi square table to see if a relationship exists between employee genders and their management level. What can you conclude at the .05 significance level?

9. Using the "Cumba" database file, develop a model to predict the employee's salary using the employee's age, years of experience, and gender. Since gender is nominal, use 0 for male and 1 for female. The "Multiple Regression" file has already been pre-loaded with the data, so you need only interpret the output. Complete the following tasks:

A. State the multiple regression equation.

B. Interpret the meaning of the slopes in the equation.

C. Predict the salary for a 40-year-old male employee with five years' experience.

D. At the .05 level of significance, determine whether each explanatory variable makes a significant contribution to the regression model.

E. Interpret the meaning of the r-squared.

F. Interpret your findings. What changes would you make to the model, given the results?

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#### Solution Summary

The solution is comprised of detailed step-by-step calculation and explanation of the various problems related to Hypothesis Tests. This solution provides students with a clear perspective of the underlying statistical aspects aspects.