To answer these questions, we need to use statistical hypothesis testing, specifically a one-sample t-test.

1. How likely it is in a sample of 250 we will find that the mean number of hours per week corporate employees work is as high as 47.

To answer this question, we need to calculate the t-score. The t-score is a ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is calculated as:

t = (X - μ) / (s/√n)

where X is the sample mean, μ is the hypothesized population mean, s is the standard deviation of the sample, and n is the sample size.

t = (47 - 40) / (3.2/√250) = 34.375

We then look up this t-score in a t-distribution table (or use a statistical software) to find the probability (p-value). A p-value less than 0.05 is typically considered statistically significant.

2. How likely it is that the true mean number of hours per week corporate employees work is 40.

This is the null hypothesis (H0: μ = 40). If the p-value is less than 0.05, we reject the null hypothesis and conclude that it is unlikely that the true mean is 40.

3. How likely it is that the true mean number of hours per week corporate employees work is more than 40.

This is the alternative hypothesis (H1: μ 40). If the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis and conclude that it is likely that the true mean is more than 40.

4. How likely it is that in a sample of 250 we will find that the mean number of hours per week corporate employees work is as high as 47 if the true mean is 40.

This is similar to the first question, but with the hypothesized mean set at 40. We would use the same t-test calculation and look up the p-value. If the p-value is less than 0.05, we would conclude that it is unlikely to find a sample mean as high as 47 if the true mean is 40.

Question

To answer these questions, we need to use statistical hypothesis testing, specifically a one-sample t-test.

1. How likely it is in a sample of 250 we will find that the mean number of hours per week corporate employees work is as high as 47.

To answer this question, we need to calculate the t-score. The t-score is a ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is calculated as:

t = (X - μ) / (s/√n)

where X is the sample mean, μ is the hypothesized population mean, s is the standard deviation of the sample, and n is the sample size.

t = (47 - 40) / (3.2/√250) = 34.375

We then look up this t-score in a t-distribution table (or use a statistical software) to find the probability (p-value). A p-value less than 0.05 is typically considered statistically significant.

2. How likely it is that the true mean number of hours per week corporate employees work is 40.

This is the null hypothesis (H0: μ = 40). If the p-value is less than 0.05, we reject the null hypothesis and conclude that it is unlikely that the true mean is 40.

3. How likely it is that the true mean number of hours per week corporate employees work is more than 40.

This is the alternative hypothesis (H1: μ > 40). If the p-value is less than 0.05, we reject the null hypothesis in favor of the alternative hypothesis and conclude that it is likely that the true mean is more than 40.

4. How likely it is that in a sample of 250 we will find that the mean number of hours per week corporate employees work is as high as 47 if the true mean is 40.

This is similar to the first question, but with the hypothesized mean set at 40. We would use the same t-test calculation and look up the p-value. If the p-value is less than 0.05, we would conclude that it is unlikely to find a sample mean as high as 47 if the true mean is 40.

Knowee AI · Accepted Answer