Question

a pet association claims that the mean annual costs of food for dogs and cats are the same. the re the two types of pets are shown below. at α = 0.05, can you reject the pet association’s claim? assu variances are equal. assume that the samples are random and independent, and the populations a distributed. complete parts (a) through (e).

dogs	cats
$s_1 = $31$	$s_2 = $28$
$n_1 = 15$	$n_2 = 19$

(a) identify the claim and state $h_0$ and $h_a$.
what is the claim?
○ a. \the mean annual cost of food for cats is greater than the cost for dogs.\
○ b. \the mean annual cost of food for dogs is greater than the cost for cats.\
○ c. \the mean annual costs of food for dogs and cats are equal.\
○ d. \the mean annual costs of food for dogs and cats are not equal.\

the null hypothesis, $h_0$, is $mu_1$ dropdown $mu_2$ the alternative hypothesis, $h_a$, is $mu_1$ dropdown $mu_2$. the claim.

Explanation:

The pet association claims the mean annual costs of food for dogs and cats are the same. Option C states this. For the hypotheses, the null hypothesis \( H_0 \) assumes equality (\( \mu_1 = \mu_2 \)) and the alternative \( H_a \) assumes inequality (\( \mu_1
eq \mu_2 \)) since we're testing if the claim (equality) can be rejected. The claim is the null hypothesis here as it's the statement being tested.

Answer:

C. "The mean annual costs of food for dogs and cats are equal."
The null hypothesis, \( H_0 \), is \( \mu_1 = \mu_2 \). The alternative hypothesis, \( H_a \), is \( \mu_1
eq \mu_2 \). The claim is the null hypothesis.