Question

a pizza delivery chain advertises that it will deliver your pizza in 30 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 30 minutes. for the simple random sample of 11 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 32.1 minutes with a standard deviation of 5.0 minutes. assume that the population distribution is approximately normal. perform a hypothesis test using a 0.05 level of significance. step 2 of 3: compute the value of the test statistic. round your answer to three decimal places.

Explanation:

Step1: Identify the formula

The formula for the one - sample t - test statistic is $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the hypothesized population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

Step2: Substitute the values

We are given that $\bar{x} = 32.1$, $\mu=30$, $s = 5.0$, and $n = 11$.
$t=\frac{32.1 - 30}{5.0/\sqrt{11}}$

Step3: Calculate the value

First, calculate $\sqrt{11}\approx3.317$. Then $5.0/\sqrt{11}\approx5.0/3.317\approx1.507$.
$t=\frac{32.1 - 30}{1.507}=\frac{2.1}{1.507}\approx1.393$

Answer:

$1.393$