Question

A consumer advocacy group suspects that a local supermarkets’s 10-ounce packages of cheddar cheese actually weight less than 10 ounces. The group took a random sample of 20 cheddar cheese packages and found the mean weight for the samples to be 9.85 ounces, with a sample standard deviation of 0.4 ounces. Based on your findings, is there enough evidence to accept the consumer advocacy groups claim at an alpha of 0.05?

Answer 1

H0: = 10

Ha: < 10

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 9.85 - 10 ) / ( 0.4 / √(20) )
t = -1.68

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 20-1) = 1.729

t > -t(α, n-1) = -1.68 > - 1.729
Result :- Fail to reject null hypothesis

We conclude that we do not have sufficient evidence to support the consumer advocacy groups claim