Question

A pizza delivery chain advertises that it will deliver your pizza in 40

minutes from when the order is placed. Being a skeptic, you decide to test and see if the mean delivery time is actually more than 40
minutes. For the simple random sample of 8
customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 47.0
minutes with a standard deviation of 7.1
minutes. Assume that the population distribution is approximately normal. Perform a hypothesis test using a 0.025
level of significance.
Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places.

Answer 1

The test statistic for the hypothesis test regarding the pizza delivery time is 3.196 when rounded to three decimal places.

Step-by-step explanation:

To compute the value of the test statistic for a hypothesis test regarding pizza delivery times, we utilize the formula for a one-sample t-test:

test statistic = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Where:
sample mean (47.0 minutes)

hypothesized population mean (40 minutes

s = sample standard deviation (7.1 minutes)

n = sample size (8 customers)

Using these values:

t = (47.0 - 40) / (7.1 / \(\sqrt{8}\))

After calculating:

t ≈ 3.196

The test statistic rounded to three decimal places is 3.196.

This test statistic helps to determine if there is significant evidence to reject the null hypothesis that the delivery time is 40 minutes in favor of the alternative hypothesis that the delivery time is more than 40 minutes, based on the sample data.