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    Regression, ANOVA, chi square test and students t test

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    1. A company has two different processes that make credit cards. Suspecting that machine B has a higher variability than machine A the manager orders a test to be run. The following data was collected:

    Machine A Machine B
    Sample size nA= 30 nB=40
    Sample Standard Deviation sA= 1.0 sB= 1.7

    a. Select the correct hypothesis to test for the difference in the variances.
    1. 2.

    3. 4.

    b. What is the critical value of the F distribution?

    c. Perform the test at the .05 level of significance. What is the observed value of the F distribution?

    d. What are your conclusions?

    2. The null hypothesis and the alternate are:
    H0: The cell categories are equal
    H1: The cell categories are not equal

    Category Observed
    A 10
    B 20
    C 30
    Assume a significance level of 5%.
    a. What is the critical value of the Chi-square?

    b. Compute the observed value of Chi-square.

    c. What is your decision regarding H0?

    3. Complete the ANOVA summary table shown here.

    Source of Variation Sum of Squares Degrees of freedom Mean Square F observed
    Between Treatments
    Error (Within Treatments)
    Sums of Squares of Total

    a. How many treatments are there?

    b. What is the total sample size?

    c. Is there a significant difference at the 5% Level of significance? Would I accept or reject the null Hypothesis. i.e. what is the critical value of the test statistic?

    5. For many years TV executives used the guideline that 30 percent of the audience were watching each of the prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 500 viewers in the Tampa St. Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainders were viewing a cable station. At the .05 significance level, can we conclude that the guideline is still reasonable?

    6. Cellulon, a manufacturer of a home insulation, wants to develop guidelines for builders and consumers regarding the effects (1) of the thickness of the insulation in the attic of a home and (2) of the outdoor temperature on natural gas consumption. In the laboratory they varied the insulation thickness and temperature. A few of the findings are:

    On the basis of the sample results, the regression equation is:
    Y_ _ 62.65 _ 1.86X1 _ 0.52X2

    a. How much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 40 degrees F?

    b. What effect would installing 7 inches of insulation instead of 6 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 40 degrees F)?

    c. Why are the regression coefficients b1 and b2 negative? Is this logical?

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    Solution Summary

    The solution gives complete steps of regression, ANOVA, chi square test and student t test problems. Null hypothesis, alternative hypothesis, critical value, test statistic and P value are given with interpretations.