You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes. You select a random sample of 64 orders. The sample mean waiting time is 4.03 minutes, with a sample standard deviation of 0.8 minutes. Complete parts (a) and (b) below.
a. Determine the test statistic.(two decimal places)
b. Find the p-value.(three decimal places)
c. What is the conclusion?

(a) The test statistics is 1.30.

(b) The P-value is 0.198.

(c) We conclude that the mean waiting time was equal to 3.9 minutes.

Step-by-step explanation:

We are given that the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes.

You select a random sample of 64 orders. The sample mean waiting time is 4.03 minutes, with a sample standard deviation of 0.8 minutes.

Let = mean waiting time at the drive-through window for branches in your geographical region.

So, Null Hypothesis, : = 3.9 minutes     {means that the mean waiting time was equal to 3.9 minutes}

Alternate Hypothesis, : 3.9 minutes     {means that the mean waiting time was different from 3.9 minutes}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                        T.S. =    ~

where, = sample mean waiting time = 4.03 minutes

            s = sample standard deviation = 0.8 minutes

            n = sample of orders = 64

So, test statistics  =    ~

                              =  1.30

(a) The value of t test statistics is 1.30.

(b) The P-value of the test statistics is given by;

            P-value = P( > 1.30) = 0.099

For two tailed test, p-value is calculated as = 0.099 2 = 0.198

(c) Since, in the question we are not given with the level of significance so we assume it to be 5%.

Now, P-value of the test statistics is more than the level of significance as 0.198 > 0.05, so we have insufficient evidence to reject our null hypothesis.

Therefore, we conclude that the mean waiting time was equal to 3.9 minutes.

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i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.