Help needed on solution steps

A medical research group is investing what differences might exist between two pain killing drugs Azerlieve and Zynumbie. The researchers have already established there is no difference between the two drugs in terms of the average amount of time required before they take effect. However, they are also interested in knowing if there is any difference between the variability of time until pain relief occurs. A random sample of 24 patients using Azerlieve and 32 patients using Zynumbie yielded the following results:

Azerlieve Zynumbie

na = 24 nz=32

sa= 37.5seconds sz = 41.3 seconds

Based on these sample data, can the researchers conclude a difference exists between the two drugs?

The 2013 graduating class from St. Francis University in Pennsylvania had the highest average student debt of all U.S. college graduates: $50,275. Second on the list was The Citadel in South Carolina, at $48,862. (Source: Susannah Snider, "10 Colleges that leave graduates with the most student loan debt," www.usnews.com, Feb. 17, 2015.) Suppose random samples of 75 St. Francis students and 205 Citadel students showed student loan standard deviations of $2,050 and $2,084, respectively. Using an alpha level of 0.10, test to determine whether the standard deviations for student loans at these two universities are equal.

The College Bookstore has four checkout stands. The store manager noticed that registers 3 and 4 served fewer students than registers 1 and 2. She is not sure whether the layout of the store channels customers into these registers, whether the checkout clerks in these lines are simply slower than in the other two, or whether she was just seeing random differences. The manager kept a record of which stands the next 1,000 students chose for checkout. The students checked out of the four stands according to the following pattern.

Stand1 338Stand2 275 Stand3 201 Stand4 186

Based on these data, can the store manager conclude that the proportions of students who use the four checkout stands are equal? (Use an =0.05.)