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 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.5 minutes and a sample standard deviation of 6 minutes. Using the critical value​ approach, at the 0.05 level of​ significance, is there evidence that the population means the delivery time has been reduced below the previous population means the value of 25 minutes?   State the null and alternative hypotheses for this test.   A. H0: μ≥25 H1: μ<25

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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 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.5 minutes and a sample standard deviation of 6 minutes.

Using the critical value​ approach, at the 0.05 level of​ significance, is there evidence that the population means the delivery time has been reduced below the previous population means the value of 25 minutes?
 
State the null and alternative hypotheses for this test.
 
A.
H0: μ≥25
H1: μ<25
 
B.
H0: μ<25
H1: μ≥25
 
C.
H0: μ>25
H1: μ≤25
 
D.
H0: μ≤25
H1: μ>25
 
E.
H0: μ≤22.5
H1: μ>22.5
 
F.
H0: μ≥22.5
h1: μ<22.5
 
What is the test statistic for this​ test?
tStat=___
 
What is the conclusion for this​ test?
 
Using the​ p-value approach, at the 0.05 level of​ significance, is there evidence that the population means the delivery time has been reduced below the previous population means the value of 25 minutes?
 
What is the​ p-value for this​ test?
 
p-value=___ (Type an integer or a decimal. Round to three decimal places as​ needed.)
 
What is the conclusion for this​ test?
 
Since the p-value is __A__ than α, __B__ the null hypothesis and conclude that there is __C__ evidence that the population means delivery time has been reduced below the previous population means value of 25 minutes.
 
A: less or greater
B: reject or do not reject
C: Sufficient or insufficient 
 
Interpret the meaning of the​ p-value in this problem. Choose the correct answer below.
 
A. The​ p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 25 minutes or​ more, given that the population means delivery time is 22.5 minutes.
 
B. The​ p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 22.5 minutes or​ less, given that the population means delivery time is 25 minutes.
 
C. The​ p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 22.5 minutes or​ more, given that the population means delivery time is 25 minutes.
 
D. The​ p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 25 minutes or​ less, given that the population means delivery time is 22.5minutes.
 
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