**Question 1:(1 reference, 1 page)**

**You have learned about the inferences about population variances, comparing multiple proportions, tests of independence and goodness of fit, and now please answer the following questions in detail by applying the knowledge that you have gained from readings and lectures of this week. It is important to include hypothetical examples whenever applicable. **

**Describe how chi squared and F random variables are generated.****What are the properties of the distribution of these random variables?****Discuss the objective in testing hypotheses on variance of one population, and variances of two populations, and the underlying assumptions.****Explain formulation of the hypothesis, the test statistic, the rationale for rejecting the null, the criterion for choosing the rejection region, possible test outcomes, and the criterion for evaluating the p value.****Provide hypothetical examples of formulating hypotheses on variance of a population, and uniformity of variance across two populations.****Explain the chi square test on uniformity of a proportion across the several populations, goodness of fit, and independence.****Explain formulation of the hypothesis, the test statistic, the rationale for rejecting the null, the criterion for choosing the rejection region, possible test outcomes, and the criterion for evaluating the p value.****Provide a hypothetical example of formulating hypotheses on uniformity of proportion across several populations.****Provide hypothetical examples of formulating hypotheses in each case.**

**Question 2(2 pages)**

**Ball bearing manufacturing is a highly precise business in which minimal part variability is critical. Large variances in the size of the ball bearings cause bearing failure and rapid wear-out. Production standards call for a maximum variance of .0001 inches. Gerry Liddy has gathered a sample of 15 bearings that shows a sample standard deviation of .014 inches. Use ɑ = .10****Please determine whether the sample indicates that the maximum acceptable variance is being exceeded.****What is the p value?**

**2. The grade point averages of 352 students who completed a college course in financial accounting have a standard deviation of .940. The grade point averages of 73 students who dropped out of the same course have a standard deviation of .797. **

**Does the data indicate a difference between the variances of grade point averages for students who completed a financial accounting course and students who dropped out?****Use ɑ = .05 level of significance.****What is the p value?**

**Note: F of alpha / 2 with degrees of freedom 351 and 72 which yields 0.025 area under its graph to the right is 1.466**