Question

A grocery store claims that customers spend an average of 6 minutes waiting for service at the​ store's deli counter. A random sample of 40 customers was timed at the deli​ counter, and the average service time was found to be 6.5 minutes. Assume the standard deviation is 1.8 minutes per customer. Using α=0.05, complete parts below.

a. Does this sample provide enough evidence to counter the claim made by the​ store's management?

Determine the null and alternative hypotheses.

H_{0_____}

H_{1_____}

The​ z-test statistic is_______

​(Round to two decimal places as​ needed.)

The critical​ z-score(s) is(are)_________

​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

Because the test statistic (falls/does not fall) within the critical values, (accept/reject) the null hypothesis.

b. Determine the​ p-value for this test.

The​ p-value is______

Answer 1

To Test :-

H0 :-  

H1 :-

Test Statistic :-


Z = 1.7568   1.76

Test Criteria :-
Reject null hypothesis if

Critical value Z < - 1.96 OR Z > 1.96

Result :- Fail to reject null hypothesis

Decision based on P value

P value =2 * P ( Z > 1.76 ) = 2 * [ 1 - P ( Z < 1.76 ) ] = 0.07895

Reject null hypothesis if P value < level of significance

0.07895 > 0.05, hence fail to reject null hypothesis

Accept Null Hypothesis

H0 :-  

There is sufficient evidence to support the claim that customers spend an average of 6 minutes waiting for service at the​ store's deli counter.