Question

Hypothesis tests for a population mean with standard deviation known

Use the information below to answer all questions:
At a large company, the attitudes of workers are'regularly measured with a standard test. The scores on the test are from 0 to 100 with higher score indicating greater satisfaction. The mean score over all company's employees was 74, with a standard deviation of 8. Some time ago, the company adopted the policy that workers could spend one day per week working form home. After the policy had been in place for some time, a random sample of 80 workers was given the test. The sample mean was 76. Assume that the standard deviation is still 8. Can we conclude that the mean level of satisfaction is different since the policy change at the alpha = 0.05 level?
a. Yes
b. No

Answer 1

The question involves hypothesis testing for a population mean with a known standard deviation to determine if worker satisfaction changed after a policy allowing remote work. Using a z-test and the sample data provided, we compare against the alpha level of 0.05 to conclude if there's a significant difference.

Step-by-step explanation:

To assess whether the mean level of worker satisfaction at a large company has changed after a policy change allowing workers to spend one day per week working from home, we use hypothesis testing for a population mean with a known standard deviation. With a previous mean score of 74, standard deviation of 8, and a sample mean of 76 from 80 workers after the policy change, we perform a two-tailed z-test to determine the statistical significance at the alpha level of 0.05.

The null hypothesis (H0) would state that there is no difference in mean satisfaction scores before and after the policy change (mu = 74), while the alternative hypothesis (Ha) would suggest there is a difference (mu does not equal 74). Using a z-test calculation, we determine the z-score corresponding to our sample mean. If this z-score corresponds to a p-value less than 0.05, we reject the null hypothesis, indicating the policy may have had an effect on satisfaction. Otherwise, we cannot conclude there has been a change.