# Hypothesis Testing & Regression Analysis

Please answer the 11 questions posted.

1. A production manager is conducting a Z test of her assembly line. She collects a sample of 64 items from the assembly line and determines that the test's critical value is +1.96 and the Z statistic is +1.73. Based on this information she should (circle one): Accept Reject the Null hypothesis.

2. Smith Widget Company makes widgets for the medical industry. One particular customer requires widgets that meet FDA standards. One FDA standard requires Z-testing of at least 100 widgets at a time at the .08 level of significance. The specific standard requires that widgets be no smaller than a certain tolerance and no larger than a certain tolerance. The critical value(s) for such a test would be: __________

3. The same production manager in question 1 above decides to use a smaller sample size of just 25 items. If she conducts a 2-tailed test at the 90 percent level of confidence, her critical value(s) would be: ________

4. National Packing Materials Company claims its X20 box can hold loads up to at least 80 pounds. Smith Widget Company has been using the boxes for one year and feels the boxes fail at lighter loads. Hearing the complaints from Smith, the lead engineer for National Packaging decides to test the company's claim that it can hold at least 80 pounds. He decides to text 64 boxes at the .05 level of significance. He finds a mean of 78 pounds with a standard deviation of 5 pounds. What is the critical value for this test?_______ What is the value of the test statistic? ___________ What is the Null hypothesis? ___________ What is the alternate hypothesis? ____________ What is the standard error of the mean? ______________ Should the Null hypothesis be accepted or rejected? __________

5. The following information was gathered for a One-Way ANOVA test at the .05 level of significance:

Treatment 1 Treatment 2 Treatment 3

9 13 10

7 20 9

11 14 15

9 13 14

12 12 15

The critical value for this test is (circle one) : a. 3.68 b. 3.34 c. 3.18 d. 3.89

6. What is the value of the F statistic in the ANOVA test in question 5 above? _____

7. True or False. A data set resulted in a regression equation of Y = 17.08 - 1.16x From the equation we can determine that the X variable is directly related to the Y variable.

8. A technique used to arrive at the regression equation by minimizing the sum of the squares of the vertical differences between the actual Y values and the predicted Y values is known as the ______________.

9. A condition that occurs in multiple regression analysis if the independent variables are themselves correlated is known as: a. autocorrelation b. stepwise regression

c. multicorrelation d. multicollinearity

10. James Profit wants to take National Widget Company public. He is interested in the relationship between the size of the initial public offering and the price per share. A sample of 10 companies that recently went public revealed the following information:

size ($millions) price per share

9.0 10.0

13.0 12.4 a. The regression equation is: __________

11.0 10.5

14.0 12.8 b. The coefficient of correlation is: ______

8.0 13.6

9.0 11.5 c. The coefficient of determination is: ____

10.0 14.2

12.0 9.7 d. What would Y equal if X equals13? ______

10.0 12.3

7.0 9.6

11. A survey of industrial salespeople who are either self-employed, work for small, medium-sized, or large firms revealed the following with respect to incomes:

Of those who earn less than $20,000, 9 are self-employed, 12 are employed by small firms, 40 by medium size firms, and 89 by large firms.

Of those who earn $20,000 to $39,999, 11 are self-employed, 10 are employed by small firms, 45 by medium size firms, and 104 by large firms.

Of those who earn $40,000 or more, 10 are self-employed, 13 are employed by small firms, 50 by medium size firms, and 107 by large firms.

Using the .05 level of significance, use a chi-square test to test the hypothesis that there is no relationship between the income level of the industrial salespeople and their employment status. Be sure to state the critical value, the test statistic value, and your interpretation of the test results.

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.