Question

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

claim: $\sigma^2 \geq 8.0$; $\alpha = 0.05$
sample statistics: $s^2 = 7.09$, $n = 22$

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

Explanation:

Step1: Identify Null Hypothesis

The claim is \( \sigma^2 \geq 8.0 \), so the null hypothesis \( H_0 \) takes the claim's inequality (or equality for null). Thus, \( H_0: \sigma^2 \geq 8.0 \).

Step2: Identify Alternative Hypothesis

The alternative hypothesis \( H_a \) is the complement of \( H_0 \) for a left - tailed or right - tailed test. Since \( H_0 \) is \( \sigma^2 \geq 8.0 \), \( H_a \) is \( \sigma^2 < 8.0 \).

Answer:

\( H_0:\sigma^2 \geq 8.0 \)
\( H_a:\sigma^2 < 8.0 \)