Question

A sample mean, sample standard deviation, and sample size are given. Perform the required hypothesis test about the mean, μ, of the normal population from which the sample was drawn. , , n = 15, H0: μ = 32.6, Ha: μ ≠ 32.6, α = 0.05. Test statistic: t = 2.66. Critical values: t = ±2.145. Reject H0. There is sufficient evidence to support the claim that the mean is different from 32.6. Test statistic: t = 2.66. Critical values: t = ±1.96. Reject H0. There is sufficient evidence to support the claim that the mean is different from 32.6. Test statistic: t = 2.66. Critical values: t = ±1.96. Do not reject H0. There is not sufficient evidence to support the claim that the mean is different from 32.6. Test statistic: t = 2.66. Critical values: t = ±2.145. Do not reject H0. There is not sufficient evidence to support the claim that the mean is different from 32.6.

Answer 1

Explanation:

The null hypothesis is

H0: μ = 32.6

The alternative hypothesis is

Ha: μ ≠ 32.6

The calculated test statistic is 2.66 for the right tail and - 2.66 for the left tail

Since the critical values for both tails is ± 2.145, we would compare the critical values with the test statistic values

In order to reject the null hypothesis, the test statistic must be smaller than - 2.145 or greater than 2.145

Since - 2.66 < - 2.145 and 2.66 > 2.145, we would reject the null hypothesis.

Therefore, Reject H0. There is sufficient evidence to support the claim that the mean is different from 32.6.

2) Test statistic: t = 2.66. Critical values: t = ±1.96

Since - 2.66 < - 1.96 and 2.66 > 1.96, we would reject the null hypothesis. Then

Reject H0. There is sufficient evidence to support the claim that the mean is different from 32.6.