QuestionA pet association claims that the mean annual costs of food for dogs and cats are the same. The results for samples or the two types of pets are shown below. At $\alpha=0.05$, can you reject the pet association's claim? Assume the oopulation variances are equal. Assume that the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e). \begin{tabular}{|l|l|} \hline \multicolumn{1}{|c|}{ Dogs } & \multicolumn{1}{c|}{ Cats } \\ \hline $\bar{x}_{1}=\$ 257$ & $\bar{x}_{2}=\$ 230$ \\ $s_{1}=\$ 31$ & $s_{2}=\$ 27$ \\ $n_{1}=16$ & $n_{2}=17$ \\ \hline \end{tabular} D. The rejection regions are $t<-2.04$ and $t>2.04$. (c) Find the standardized test statistic. $\mathrm{t}=2.67$ (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. $\square$ Reject the null hypothesis because the test statistic is $\square$ in a/the rejection region. (e) Interpret the decision in the context of the original claim.
At the $5 \%$ significance level, $\square$ enough evidence to $\square$ the claim that the mean annual cost of food for dogs is $\square$ the mean annual cost of food for cats.