use a $\chi^2$-test to test the claim $\sigma^2 = 0.55$ at the $\alpha = 0.10$ significance level using sample statistics $s^2 = 0.526$ and $n = 18$. assume the population is normally distributed. identify the null and alternative hypotheses. $\bigcirc$ a. $h_0: \sigma^2 = 0.55$ $h_a: \sigma^2 \ eq 0.55$ $\bigcirc$ b. $h_0: \sigma^2 \geq 0.55$ $h_a: \sigma^2 0.55$ $\bigcirc$ d. $h_0: \sigma^2 \ eq 0.55$ $h_a: \sigma^2 = 0.55$

Question

use a $\chi^2$-test to test the claim $\sigma^2 = 0.55$ at the $\alpha = 0.10$ significance level using sample statistics $s^2 = 0.526$ and $n = 18$. assume the population is normally distributed. identify the null and alternative hypotheses. $\bigcirc$ a. $h_0: \sigma^2 = 0.55$ $h_a: \sigma^2 \
eq 0.55$ $\bigcirc$ b. $h_0: \sigma^2 \geq 0.55$ $h_a: \sigma^2 < 0.55$ $\bigcirc$ c. $h_0: \sigma^2 \leq 0.55$ $h_a: \sigma^2 > 0.55$ $\bigcirc$ d. $h_0: \sigma^2 \
eq 0.55$ $h_a: \sigma^2 = 0.55$

Accepted Answer

# Brief Explanations:
The null hypothesis ($H_0$) is a statement of equality or no change, and the alternative hypothesis ($H_a$) is what we might believe if we reject $H_0$. The claim here is $\sigma^2 = 0.55$, so the null hypothesis should be $H_0: \sigma^2 = 0.55$. Since there's no indication of a one - tailed test (greater than or less than), the alternative hypothesis is a two - tailed test, $H_a: \sigma^2
eq0.55$. This matches option A.
# Answer:
A. $H_0:\sigma^{2}=0.55$, $H_{a}:\sigma^{2}
eq0.55$

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