A pizza place recently hired additional drivers and as a result now claims that its average delivery time for orders is under 44 minutes. A sample of 39 customer deliveries was examined, and the average delivery time was found to be 40.5 minutes. Historically, the standard deviation for delivery time is 11.3 minutes. Using alphaequals0.05, complete parts a and b below. a. Does this sample provide enough evidence to support the delivery time claim made by the pizza place? Determine the null and alternative hypotheses. Upper H 0: mu greater than or equals 44 Upper H 1: mu less than 44 The z-test statistic is negative 1.93. (Round to two decimal places as needed.) The critical z-score(s) is(are) 1.64 comma negative 1.64. (Round to two decimal places as needed. Use a comma to separate answers as needed.)

We are given that a pizza place recently hired additional drivers and as a result now claims that its average delivery time for orders is under 44 minutes.

A sample of 39 customer deliveries was examined, and the average delivery time was found to be 40.5 minutes. Historically, the standard deviation for delivery time is 11.3 minutes.

From this, X bar = 40.5 , [tex]\sigma[/tex] = 11.3 , [tex]\mu[/tex] = 44 and sample, n = 39

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] >= 44

Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] < 44

The test statistics used here will be;

T.S. = [tex]\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

So, Test statistics = [tex]\frac{40.5-44}{\frac{11.3}{\sqrt{39} } }[/tex] = -1.93

Now, at 5% significance level the z score table gives critical value of -1.6449 as it is one-tail test.

Since our test statistics is less than the critical value as -1.93 < -1.6449, so we have sufficient evidence to reject null hypothesis and conclude that the average delivery time for orders is under 44 minutes.