A tax specialist knows that tax refunds for people who use a firm to do their tax returns are normally distributed with a mean of $150 and a standard deviation of
$43. The specialist believes that the company, Taxco, uses under trained staff and gets a lower average tax refund for its customers. He takes a random sample of 6 customers from Taxco’s records and finds the following refunds:
Refund($)144,38,130,160,81,135
Run a full hypothesis test at the 5% level of significance to test the tax specialists belief about Taxco.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
I'll let you do the calculations.