Chapter 11.6, Problem 15PPS

To determine

Identify the hypothesis and claim.

Answer to Problem 15PPS

  $H_0:\mu \ge 30$ , $H_a:\mu <30$ (claim); do not reject $H_0$ ; there is not enough evidence to support the pizza chain’s claim of delivery time of less than $30$ minutes.

Explanation of Solution

Given information:

A pizza chain promises a delivery time of less than $30$ minutes, using a sample of $38$ deliveries, Chelsea calculated a mean delivery time of $29.6$ minutes with a standard deviation of $3.9$ minutes. Test the hypothesis at $1\%$ significance.

Calculation:

Consider null hypothsis $H_0$ and alternative hypothesis is $H_a$ . It is given as,

  $\begin{array}{l}{H}_0:\mu \ge 30\\ H_a:\mu <30\end{array}$

The claim is $H_a:\mu <30$ it is alternative hypothesis and it is not equality. The null hypothesis is $H_0:\mu \ge 30$ is competent of $H_a:\mu <30$ .

The hypothesis test for alternative $\mu <30$ is a left trailed test. Now test at $1\%$ significance.

Use $TI83$ calculator for value calculation,

Press $key{2}^{nd}$ and then DISTR. Choose $3^{rd}$ option.

  

Now calculate $Z-statistic$ for sample data,

  $z=\frac{\overline{x}-\mu }{\left(\frac{s}{\sqrt{n}}\right)}\mathrm{.....}\left(1\right)$

Now put the values, mean is $29.6$ minutes, standard deviation of $3.9$ minutes, sample of $38$ deliveries in equation $\left(1\right)$ .

  $\begin{array}{l}z=\frac{29.6-30}{\left(\frac{3.9}{\sqrt{38}}\right)}\\ =-0.6322\end{array}$

Hence, $H_0:\mu \ge 30$ , $H_a:\mu <30$ (claim); do not reject $H_0$ ; there is not enough evidence to support the pizza chain’s claim of delivery time of less than $30$ minutes.