During Summer 2013, Procter and Gamble (P&G) recalled 30 different types of cat and dog food because they may have been contaminated with Salmonella. While pets can become ill from eating contaminated...

During Summer 2013, Procter and Gamble (P&G) recalled 30 different types of cat and dog food because they may have been contaminated with Salmonella. While pets can become ill from eating contaminated foods, the Centers for Disease Control and Prevention also reminded people to wash their hands thoroughly after handling pet food. Independent random samples of P&G cat foods and dog foods were obtained, and each was tested for Salmonella. For cat food,
 and 50 were contaminated, and for dog food,
 and 87 were contaminated. Is there any evidence to suggest that the true proportion of contaminated cat food is different from the true proportion of contaminated dog food?

The U.S. Internal Revenue Service estimates that the average taxpayer takes approximately six hours to complete Form 1040. A study was conducted to examine the amount of time it takes to complete this dreaded form, by income level. Independent random samples of federal filers in two income ranges were obtained, and the length of time (in hours) to complete Form 1040 was recorded for each. The summary statistics are given in the following table

Assume the underlying populations are normal.

a.
Conduct an F test to determine whether there is any evidence that the two population variances are different.

b.
Using your conclusion from part (a), conduct the appropriate test for evidence that the mean time to complete Form 1040 for the lower-income level is less than the mean time for the higher-income level.  State your conclusion and find bounds on the
p
value.