The social worker for a particular town claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 24 records and computes the average monthly cost of this type of childcare to be $689 with a standard deviation of $40.
a) Perform the appropriate test of hypothesis for the potential resident using = 0.01. Clearly show the eight (8) steps of hypothesis testing and draw a picture of the rejection region.
(8)
b) Find the p-value for this test. (2)
c) Based on your results above, to which type of error are you subject to, Type I or Type II? Motivate your answer. Also interpret this type of error in terms of this example.