Question

You are testing the null hypothesis that the average money that BC student has in his or her pocket is $20 against the alternative that it’s greater than that. You are testing at a 5 percent significance level. We know the population variance is 81 dollars squared. You take a random sample of 100 students.

i. Calculate the power of this test if the true mean is $23. Represent it graphically.

For parts, ii, iii, iv and v, please take the information above and change only the one item that is described. (i.e. compare part iii to our answer and values in part i, not to part ii.) Also, show me how your diagram would change if you were drawing the true distribution of sample means and the distribution under the null hypothesis.

ii. What does the power equal if we changed α to .10?

iii. What if we changed our sample size to 36?

iv. What if the population variance was really 25 dollars squared.

v. What if the true population mean is $22?

Answer 1