Question

A local bottler in Hawaii wishes to ensure that an average of 16 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 48 bottles. The mean weight of the passion fruit juice in the sample is 15.80 ounces. Assume that the population standard deviation is 0.8 ounce. Use the critical value approach to test the bottler's concern at α = 0.05. What is your conclusion?

a. Reject H0 since the value of the test statistic is not less than the negative critical value.

b. Reject H0 since the value of the test statistic is less than the negative critical value.

c. Do not reject H0 since the value of the test statistic is not less than the negative critical value.

d. Do not reject H0 since the value of the test statistic is less than the negative critical value.

Answer 1

H0: = 16

Ha: 16

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 15.8 - 16 ) / ( 0.8 / √( 48 ))
Z = -1.73
Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.05 /2 ) = -1.96 , 1.96
Since z > -1.96,
Result :- Fail to reject null hypothesis

Do not reject H0 since the value of the test statistic is not less than the negative critical value.