Question

1. Manufacturers often include “suggested retail prices” with goods that are shipped from the factories. However, retailers are not bound by these suggested prices; A manufacturer of a brand of food processor with a suggested retail price of $89.95, is curious to know if the mean price charged among all retailers is below the suggested retail price. He randomly samples 28 retail stores and records the price at which each is selling the food processor. The sample results find a mean of $87.72 and a standard deviation of $5.10.

A. Do the data provide sufficient evidence to conclude that the true mean price of the food processor is below the suggested retail price? Test at the .05 level of significance.

B. What type of error might you have made in part A? Explain fully.

Answer 1

a) H0: = 89.95

HA: 89.95

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 87.72 - 89.95 ) / ( 5.1 / √(28) )
t = -2.3137

Test Criteria :-

Reject null hypothesis if | t | > t(α/2, n-1)
Critical value t(α/2, n-1) = t(0.05 /2, 28-1) = 2.052

| t | > t(α/2, n-1) = 2.3137 > 2.052

Result :- Reject null hypothesis

b)

Since H0 is rejected , we might made type 1 error.

[ Type 1 error is H0 is rejected when infact it is true. ]