A manager of a pizza restaurant has changed the restaurant\'s delivery process i

Question

A manager of a pizza restaurant has changed the restaurant's delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 30 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 27.7 minutes and a sample standard deviation of 66 minutes. Complete parts (a) through (d) below.

What is the test statistic for this test?

What is the p-value?

Interpret the meaning of the p-value in this problem.

Compare your conclusions in (a) and (b).

Explanation / Answer

for 35 degree of freedom at 0.05 level; critical value of t for left tailed test =-2.0301

here std error=std deviation/(n)1/2 =11

hence test stat t=(X-mean)/std error =(27.7-30)/11=-0.2091

as test stat is not in critical region we can not reject null hypothesis that mean is 30 minutes

b) p value for abvoe test stat =0.4178

c) p value is the extreme probability to accept null hypothesis when it is true

as it is greater then 0.05 level  we can not reject null hypothesis that mean is 30 minutes

d) both part (A) and (b) lead to same conclusion that we do not have sufficient evidence to accept mean time has been reduced from 30 minutes

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