use a $\chi^2$-test to test the claim $\sigma \geq 39$ at the $\alpha = 0.10$ significance level using sample statistics $s = 38.6$ and $n = 12$. assume the population is normally distributed. click the icon to view the chi-square critical values table. identify the null and alternative hypotheses. $\bigcirc$ a. $h_0: \sigma \geq 39$ $h_a: \sigma 39$ $\bigcirc$ c. $h_0: \sigma 39$ $h_a: \sigma \leq 39$ $\bigcirc$ d. $h_0: \sigma

Question

use a $\chi^2$-test to test the claim $\sigma \geq 39$ at the $\alpha = 0.10$ significance level using sample statistics $s = 38.6$ and $n = 12$. assume the population is normally distributed. click the icon to view the chi-square critical values table. identify the null and alternative hypotheses. $\bigcirc$ a. $h_0: \sigma \geq 39$ $h_a: \sigma < 39$ $\bigcirc$ b. $h_0: \sigma \leq 39$ $h_a: \sigma > 39$ $\bigcirc$ c. $h_0: \sigma > 39$ $h_a: \sigma \leq 39$ $\bigcirc$ d. $h_0: \sigma < 39$ $h_a: \sigma \geq 39$

Accepted Answer

# Brief Explanations:
To identify the null and alternative hypotheses for a hypothesis test, the null hypothesis ($H_0$) typically contains the claim being tested or a statement of equality/non - strict inequality, and the alternative hypothesis ($H_a$) is the complement. Here, the claim is $\sigma\geq39$. So, the null hypothesis $H_0$ should be $\sigma\geq39$, and the alternative hypothesis $H_a$ (the complement of $H_0$) should be $\sigma < 39$, which matches option A.
# Answer:
A. $H_0:\sigma\geq39$, $H_a:\sigma < 39$

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