The Department of Health is concerned that the average percentage mark-up on a particular vitamin product is more than 40%. To test their concern, they sampled 76 pharmacies that sell the product, and found that the mean percentage mark-up was 44.1%. Assume that the population standard deviation of the percentage mark- up is 14.7%.
(a) What is the appropriate test statistic for this management scenario? Why?
(b) Formulate the null and alternative hypothesis for this test situation.
(c) Conduct an appropriate statistical test at the 1% level of significance to determine whether the Department of Health's concern is justified. What conclusion can be drawn from the findings?
(d) Use Excel's NORMSDIST function to find the p-value for the test and draw the appropriate management conclusion.