Question

A local newspaper was wondering if its average reader lived more than 25 miles from its headquarters. The newspaper surveyed its readers and received 10 responses. Using the results from the current survey and several previous surveys, the newspaper has decided to assume that the population standard deviation for the distance its readers live from its headquarters is 13.2 miles. The local newspaper conducts a one-mean hypothesis at the 5% significance level, to test if the average distance a reader lives from the newspaper's headquarters is greater than 25 miles. (a) H0:μ=25; Ha:μ>25, which is a right-tailed test. (b) z0=0.22, p-value is = 0.41. (c) Which of the following are appropriate conclusions for this hypothesis test? Select all that apply. We reject H0. We fail to reject H0. At the 5% significance level, the data provide sufficient evidence to conclude that the average distance a reader lives from the newspaper's headquarters is greater than 25 miles. At the 5% significance level, the data do not provide sufficient evidence to conclude that the average distance a reader lives from the newspaper's headquarters is greater than 25 miles.

Answer 1

Answer:

We fail to reject H₀.

At the 5% significance level, the data do not provide sufficient evidence to conclude that the average distance a reader lives from the newspaper's headquarters is greater than 25 miles.

Step-by-step explanation:

The hypothesis for the statistical test is defined as follows:

H₀ : μ =25 vs. Hₐ : μ > 25

The test statistic value is, z₀ = 0.22.

The p-value of the test is, p-value = 0.41.

The significance level is, α = 0.05.

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

A small p-value (typically ≤ 0.05) specifies strong evidence against the null hypothesis (H₀), so you discard H₀.

A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

Here, p-value = 0.41 > α = 0.05.

The null hypothesis was failed to be rejected at 5% level of significance.

Conclusion:

There is not enough evidence to support the claim that the average distance a reader lives from the newspaper's headquarters is greater than 25 miles.