Final answer:
To determine if the mean annual costs of food for dogs and cats are the same, we can conduct a hypothesis test using a two-sample t-test.
Step-by-step explanation:
To determine if the mean annual costs of food for dogs and cats are the same, we can conduct a hypothesis test. We can use a two-sample t-test since we have two independent samples. The null hypothesis is that the mean annual costs are the same, and the alternative hypothesis is that they are different.
We calculate the test statistic using the formula: t = (mean1 - mean2) / sqrt((s1^2 / n1) + (s2^2 / n2)), where mean1 is the mean annual cost for dogs, mean2 is the mean annual cost for cats, s1 is the standard deviation for dogs, n1 is the sample size for dogs, s2 is the standard deviation for cats, and n2 is the sample size for cats.
We then use the t-distribution to find the p-value associated with the test statistic. If the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference in the mean annual costs of food for dogs and cats.