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. $\text{h}_a: \sigma^2 \ eq 0.55$ $\text{h}_a: \sigma^2 0.55$ $\text{h}_a: \sigma^2 = 0.55$ identify the standardized test statistic. 16.26 (round to two decimal places as needed.) identify the critical value(s). 8.67,27.59 (round to two decimal places as needed. use a comma to separate answers as needed.) choose the correct conclusion below. $\text{o a. }$ fail to reject $\text{h}_0$. there is enough evidence at the 10% level of significance to reject the claim. $\text{o b. }$ fail to reject $\text{h}_0$. there is not enough evidence at the 10% level of significance to reject the claim. $\text{o c. }$ reject $\text{h}_0$. there is not enough evidence at the 10% level of significance to reject the claim. $\text{o d. }$ reject $\text{h}_0$. there is enough evidence at the 10% level of significance to reject the claim.

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.

$\text{h}_a: \sigma^2 \
eq 0.55$ $\text{h}_a: \sigma^2 < 0.55$
$\text{o c. } \text{h}_0: \sigma^2 \leq 0.55$ $\text{o d. } \text{h}_0: \sigma^2 \
eq 0.55$
$\text{h}_a: \sigma^2 > 0.55$ $\text{h}_a: \sigma^2 = 0.55$

identify the standardized test statistic.
16.26 (round to two decimal places as needed.)

identify the critical value(s).
8.67,27.59
(round to two decimal places as needed. use a comma to separate answers as needed.)

choose the correct conclusion below.
$\text{o a. }$ fail to reject $\text{h}_0$. there is enough evidence at the 10% level of significance to reject the claim.
$\text{o b. }$ fail to reject $\text{h}_0$. there is not enough evidence at the 10% level of significance to reject the claim.
$\text{o c. }$ reject $\text{h}_0$. there is not enough evidence at the 10% level of significance to reject the claim.
$\text{o d. }$ reject $\text{h}_0$. there is enough evidence at the 10% level of significance to reject the claim.

Accepted Answer

# Explanation:
## Step1: Recall Hypothesis Testing Rules
The null hypothesis $ H_0 $ contains the claim being tested (equality), and the alternative hypothesis $ H_a $ is the complement. Here, the claim is $ \sigma^2 = 0.55 $, so $ H_0: \sigma^2 = 0.55 $ and $ H_a: \sigma^2
eq 0.55 $ (two - tailed test, though the options here seem to have some formatting issues, but for the conclusion part:

## Step2: Compare Test Statistic and Critical Values
The test statistic is $ \chi^2 = 16.26 $, and the critical values are $ 8.67 $ and $ 27.59 $. We check if the test statistic lies between the critical values. Since $ 8.67<16.26<27.59 $, we fail to reject $ H_0 $. Failing to reject $ H_0 $ means there is not enough evidence at the $ \alpha = 0.10 $ level to reject the claim (which is in $ H_0 $).

# Answer:
B. Fail to reject $ H_0 $. There is not enough evidence at the 10% level of significance to reject the claim.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall Hypothesis Testing Rules

Step2: Compare Test Statistic and Critical Values

Answer: