Question

You are the owner of a restaurant that delivers pizza to university dormitory. You have just changed your delivery process to reduce the mean time between the order and delivery completion. 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. Previous mean value of delivery time was 25 minutes. You want to see if there is evidence that the mean delivery time has been reduced below previous mean value of 25 minutes.

a. State the null and alternative hypothesis. You can use the symbols tab (after Q5) to copy the symbols you need.

H0:

HA:

b. At the 0.05 level of significance, is there evidence that the mean delivery time has been reduced below previous mean value of 25 minutes? Show all the steps!

Answer 1

a. $H_0:\mu=25$ vs $H_1:\mu<25$

b. Here n=36 so we will use z distribution

$z=\frac{22.4-25}{\frac{6}{6}}=-2.6$

P value is $P(z<-2.6)=0.0047$

As P value is less than alpha=0.05 we reject the null hypothesis