Question

A report states that the average U.S. Certified Public Accountant (CPA) works 60 hours per week during tax season. We want to determine if CPAs in states with flat state income tax rates work less than 60 hours per week on average. Suppose from previous studies it is known that the standard deviation for the number of hours worked during tax season is 27.4 hours per week. We plan to conduct the test at the .10 level of significance based on a random sample of 150 CPAs in states with a flat state income tax rate. a) What is the power of the test to correctly identify a decrease in the mean number of hours worked in states with a flat state income tax rate if the actual mean number of hours worked in these states is 55? ( how a Type II Error is calculated. Write out the solution in steps) b) Give a practical interpretation of the probability you found in part (a), in the context of the problem.

Answer 1

To calculate the power of a hypothesis test, we need to determine the probability of correctly identifying a decrease in the mean number of hours worked in states with a flat state income tax rate when the actual mean number of hours worked is 55.

Step-by-step explanation:

To calculate the power of a hypothesis test, we need to determine the probability of correctly identifying a decrease in the mean number of hours worked in states with a flat state income tax rate when the actual mean number of hours worked is 55. The power of the test is the probability of rejecting the null hypothesis (that the mean number of hours is equal to 60) when the alternative hypothesis (that the mean number of hours is less than 60) is true.

To calculate the power, we need to find the test statistic, which follows a t-distribution with (n-1) degrees of freedom. In this case, n = 150. We can use the t-distribution to determine the critical value for a one-sided test at the 0.10 level of significance. Assuming a normal distribution, we can calculate the test statistic:

t = (sample mean - population mean) / (standard deviation / sqrt(n)) = (55 - 60) / (27.4 / sqrt(150))

Then, we can calculate the probability of observing a test statistic less than the critical value:

power = P(t < critical value) = P(t < t_critical) = P(t < t_critical, df = 149)

Using a t-distribution table or a statistical software, we can find the t_critical value for a one-sided test with 149 degrees of freedom and a significance level of 0.10. Finally, we calculate the power using the t_critical value and the t-distribution:

power = P(t < t_critical, df = 149)