Question

A pet association claims that the mean annual cost of food for dogs and cats are the same. The results for samples for the two types of pets are shown below. Is there enough evidence at ? = 0.05 to reject the pet association’s claim? Assume the population variances are not equal. Assume the samples are random and independent and the populations are normally distributed.

Dogs Cats

?̅̅1̅ = $210    ?̅̅2̅ = $187

?1 = 35 ?1 = 31

?1 = 17 ?1 = 9

A. State the claim mathematically. Is the claim the null or alternative hypothesis?

B. State your hypotheses.

C. Determine the test of significance (t-test or z-test) and justify your choice.

D. State the standardized test statistic.

E. State the p-value.

F. State the correct decision of the test.

G. Interpret the decision in the context of the claim.

Answer 1

Solution:

A. The claim is:

It is the null hypothesis.

B. The null and alternative hypothesis.

C. We will be using the t-test because the population standard deviations are unknown

D. The test statistic is:

  

E. The p-value is:

F. Fail to reject the null hypothesis because the p-value is greater than the significance level.

G. Since we fail to reject the null hypothesis, therefore, there is not sufficient evidence to warrant the rejection of the claim that the mean annual cost of food for dogs and cats are the same.