Question

You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

A) Using the six-step critical value approach, at the 0.05 level of significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 25 minutes?
B) At the 0.05 level of significance, use the five-step P-value approach.
C) Interpret the meaning of the P-value in (b).
D) Compare your conclusions in (a) and (b).

Answer 1

a) Critical value Approach

The hypothesis are:

Rejection region:

Reject Ho if Z < -Z _0.05 =-1.65(Critical value at 95 % for left tailed test is -1.65

Test ststistic:

Conclusion:

Since the Z score calculated < Z score critical value hence we reject the null hypothesis and conclude that there is enough evidence to suport the claim.

b) P-value approach

The hypothesis are:

Rejection region:

Reject Ho if Z < -Z _0.05 =-1.65(Critical value at 95 % for left tailed test is -1.65

Test ststistic:

P-value:

P-value calcuated at Z score computed above is calculated uisng Z table shown below as

P-value= 0.0047

Conclusion:

Since the p-value calculated < level of significance hence we reject the null hypothesis and conclude that there is enough evidence to suport the claim.

c) P-value states that the happening of that event is very low hence it follows rare event rule which concludes in rejecting the null hypothesis and in suppporting the claim.

d) Both the conclusions are same