Question

A survey collected data from a random sample of 121 people fiving in Jade city. The sample average of the distance people travel to reach their workplaces ( Yˉ ) is 23.28 km and the standard devlation (s Y​ ) is 7.48 km. The standard error of the sample average of the distance people travel to reach their workplaces is km. (Round your answer to two decimal places.) Let μy denote the mean of the distance all the people in Jade city travel to reach their workplaces. The p-value of the test H 0​ :μ y​ =22 km vs. H 1​:μY​ ≠22 km is (Round your answer to two decimal places.)

Answer 1

The standard error of the sample average of the distance people travel to reach their workplaces is 0.68 km. The p-value of the test H₀: μᵧ = 22 km vs. H₁: μᵧ ≠ 22 km is 0.028.

Step-by-step explanation:

The standard error of the sample average distance people travel to work in Jade city is 0.68 km. Conducting a hypothesis test comparing the sample mean (23.28 km) to the hypothesized population mean (22 km), the calculated z-score is approximately 2.12.

This results in a two-tailed p-value of 0.028. As the p-value is less than the commonly used significance level of 0.05, we reject the null hypothesis. This implies that the mean distance people in Jade city travel to reach their workplaces significantly differs from 22 km, providing statistical evidence for this assertion based on the collected sample data.

The standard error captures the variability of the sample mean from the population mean, and the calculated p-value helps determine the significance of this difference, supporting the rejection of the null hypothesis in favor of the alternative hypothesis.