Question

You are asked to conduct a hypothesis test for the following null and alternative hypotheses regarding mean postgraduate earnings: null: mu =$50,000 alternative: mune $50,000 You collect a sample of 100 graduates and calculate the sample mean and sample standard deviation of postgraduate earnings. Using this sample, you end up rejecting the null hypothesis at the 5% significance level. Suppose we later find out that the mean postgraduate earnings in the college student population is $50,000. What error has been committed here ?

A) We failed to reject a false null
B) We calculated the incorrect value of the test statistic
C) There is no error committed
D) We chose an incorrect significance level
E)We rejected the true null

Answer 1

If after rejecting the null hypothesis at a 5% significance level it is discovered that the population mean is indeed $50,000, a Type I error has been made as the true null hypothesis was incorrectly rejected.

Step-by-step explanation:

When conducting a hypothesis test and the result leads to rejecting the null hypothesis, this can sometimes result in a Type I error. A Type I error occurs when the null hypothesis is actually true, but it is rejected based on the sample data. From the information you've provided, the null hypothesis specified was that the mean postgraduate earnings (mu) are equal to $50,000, and it was rejected based on the sample data at a 5% significance level.

However, if the true population mean was later confirmed to be $50,000, it indicates that a Type I error was committed. Therefore, the correct answer is E) We rejected the true null.