Question

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. Use a 5% significance level. Perform a hypothesis test to determine whether there has been a decrease in the average number of customers visiting the dealership daily. Show all steps in the step-by-step procedure.

Answer 1

Ho :- mu = 800

Ha :- mu < 800

Xbar=750 , n=100, sigma =350 , alpha = 0.05

This is one sample mean Z test

Test statistics

Z = ( xbar - mu ) / ( sigma / sqrt ( n ) )

Z = ( 750 - 800 ) / ( 350 / sqrt ( 100 ) )

Z = -1.4286

Decision rules

Reject Ho if

Z stat < Z critical

Z = - 1.4286 > - 1.645 = Z critical

We do not reject Ho

P value = P ( Z < - 1.4286 ) = 0.0766

P value = 0.0766 > 0.05 = alpha

We do not reject Ho

Conclusion :- there is not sufficient evidence to support the claim that the financial crisis decreased the number of customers visiting her dealership at 0.05