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 3 of 3: draw a conclusion and interpret the decision. answer we reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the mean delivery time is actually more than 30 minutes. we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the mean delivery time is actually more than 30 minutes. we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the mean delivery time is actually more than 30 minutes. we reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the mean delivery time is actually more than 30 minutes.

Explanation:

Step1: Calculate the test - statistic

The null hypothesis $H_0:\mu\leq30$ and the alternative hypothesis $H_1:\mu > 30$. The test - statistic for a one - sample t - test is $t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}$, where $\bar{x} = 32.1$, $\mu_0=30$, $s = 5.0$, and $n = 11$. So $t=\frac{32.1 - 30}{5.0/\sqrt{11}}\approx\frac{2.1}{1.5075}\approx1.39$.

Step2: Determine the critical value

The degrees of freedom is $df=n - 1=11 - 1 = 10$. For a one - tailed test with $\alpha = 0.05$ and $df = 10$, the critical value $t_{\alpha,df}=t_{0.05,10}=1.812$.

Step3: Make a decision

Since the calculated $t$ - value ($1.39$) is less than the critical value ($1.812$), we fail to reject the null hypothesis.

Answer:

We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the mean delivery time is actually more than 30 minutes.