Question

A Burger King's manager claims their ¼ pound hamburgers actually weigh an average of over a ¼ pound before cooking. Furthermore, he knows that the population standard deviation is 0.08 of a pound. To test if this is true, you randomly buy 30 hamburger patties and weigh them. You find the sample mean weight is .265.

a) Run thetest at the 5% significance level using a p-value

b) Find the rejection regionfor the test

Answer 1

H0 :- µ = 0.25
H1 :- µ > 0.25

Part a)

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 0.265 - 0.25 ) / ( 0.08 / √( 30 ))
Z = 1.027

P value = P ( Z < 1.027 ) = 0.1522 ( from Z table )

Decision based on P value
Reject null hypothesis if P value < α = 0.05 level of significance
Since 0.1522 > 0.05 ,hence we reject null hypothesis
Result :- We fail to reject null hypothesis

There is insufficient evidence to support the claim that hamburgers actually weigh an average of over a ¼ pound before cooking.

Part b)

Reject null hypothesis if Z > Z(α)
Critical value Z(α) = Z(0.05) = 1.645

Z > 1.645 ( rejection region )