Question

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.)

Answer 1

Answer:

Yes, this sample provide enough evidence to support the delivery time claim made by the pizza​ place.

Step-by-step explanation:

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 ,   $\sigma$ = 11.3   , $\mu$ = 44   and    sample, n = 39

     Null Hypothesis, $H_0$ : $\mu$ >= 44

Alternate Hypothesis, $H_1$ : $\mu$ < 44

The test statistics used here will be;

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

So, Test statistics = $\frac{40.5-44}{\frac{11.3}{\sqrt{39} } }$ = -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.