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.
$h_0: \sigma^2 = 34.9$
$h_a: \sigma^2 \
eq 34.9$
(type integers or decimals. do not round.)

calculate the standardized test statistic.
$\chi^2 = 97.22$ (round to two decimal places as needed.)

determine the p - value.
p - value = 0.566 (round to three decimal places as needed.)

decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the claim.
$h_0$. there enough evidence at the 5% level of significance to the claim.

Explanation:

Step1: Compare P - value and \(\alpha\)

We know that \(\alpha = 0.05\) and the P - value \(= 0.566\). Since \(0.566>0.05\), we fail to reject the null hypothesis \(H_0\).

Step2: Interpret the result

When we fail to reject \(H_0\), it means that there is not enough evidence at the 5% level of significance to support the claim (because the claim is the alternative hypothesis \(H_a:\sigma^{2}
eq34.9\) and we did not have enough evidence to reject the null hypothesis which is the opposite of the claim in terms of the test).

Answer:

Fail to reject \( H_0 \); is not; support