Homework SourseYou are the manager of a restaurant that delivers pizza to c
You are the manager of a restaurant that delivers pizza to college dorm 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.
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?
At the 0.05 level of significance , use the five step p-value approach and interpret the meaning of the p-value.
Compare your conclusions in part 1 and 2
Requirements for the assignment:
Write at least a 50 word explanation.
Solution
Formulating the null and alternative hypotheses,
Ho: u >= 25
Ha: u < 25
As we can see, this is a left tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = - 1.644853627
Getting the test statistic, as
X = sample mean = 22.4
uo = hypothesized mean = 25
n = sample size = 36
s = standard deviation = 6
Thus, z = (X - uo) * sqrt(n) / s = -2.6
Comparing z < -1.644, we REJECT THE NULL HYPOTHESIS.
Also, the p value is
p = 0.004661188
Comparing p < 0.05, we REJECT THE NULL HYPOTHESIS.
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Thus, there is significant evidence that the mean time of delivery was reduced.
We got the same conclusion for the critical value test and the p value test, because they are basically the same test.
The critical marks exactly 0.05 P value. Thus, if you go further than the critical value, then the P value will become smaller as well. Both of these will lead you to reject the null hypothesis in this case.
