Thousands of people nationwide are going to get together and do a fundraiser for

Question

Thousands of people nationwide are going to get together and do a fundraiser for the American Cancer Society. The goal is to have each person raise $100 (or more). In a random sample of 40 people, an average of $120 dollars was raised, with a standard deviation of $7.50. The significance level is 1%.

What is the value of the test statistic, rounded to three decimal places?

Does the data provide enough evidence to suggest the goal is not being met?

What is the critical value?

Should you reject or fail to reject the null hypothesis?

Please show work!

Explanation / Answer

we have to do this question by hypothesis test and all the parts will be answered collectively in the solution

We need to test the null H0 : µ < 100

against the one-sided alternative H1 : µ >= 100, at level = 0.01.

Since n is large, we will do a large-sample z-test. The rejection region or the critical region is Z > z = 2.33, using the normal table.

Z = (X µ0) /(S/ n) = (120-100)/(7.5/sqrt(40)) = 16.86 Since Z = 16.86 > 2.33, H0 is rejected. Thus, there is significant evidence at 1% signifi- cance level that the mean are above 100

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