Question

test the claim about the population variance $\sigma^2$ at the level of significance $\alpha$. assume the population is normally distributed.

claim: $\sigma^2 \
eq 34.9$; $\alpha = 0.05$
sample statistics: $s^2 = 37.7$, $n = 91$

write the null and alternative hypotheses.
$h_0: \sigma^2 \square$
$h_a: \sigma^2 \square$
(type integers or decimals. do not round.)

Explanation:

Step1: Determine Null Hypothesis

The null hypothesis \( H_0 \) is a statement of equality. For a claim about population variance \( \sigma^2
eq 34.9 \), the null hypothesis assumes the opposite of the alternative in terms of equality. So \( H_0: \sigma^2 = 34.9 \).

Step2: Determine Alternative Hypothesis

The alternative hypothesis \( H_a \) matches the claim. The claim is \( \sigma^2
eq 34.9 \), so \( H_a: \sigma^2
eq 34.9 \).

Answer:

\( H_0: \sigma^2 = 34.9 \)
\( H_a: \sigma^2
eq 34.9 \)