Chapter 10.2, Problem 10.41E

To determine

To Explain: the state null hypothesis and alternative hypothesis carry out the test.

Answer to Problem 10.41E

There is enough evidence to support the claim that the mean amount charged increases under the no-fee offer.

Explanation of Solution

Given:

  $\begin{array}{c}n=200\\ \overline{x}=332\\ s=108\\ \alpha =1\%=0.01\end{array}$

Formula used:

  $z=\frac{\overline{x}-\mu }{\sigma /\sqrt{n}}$

Calculation:

The claim is either the null hypothesis or the alternative hypothesis

  $\begin{array}{c}{H}_0:\mu =0\\ H_1:\mu >0\end{array}$

  $\begin{array}{c}z=\frac{\overline{x}-\mu }{\sigma /\sqrt{n}}\\ =\frac{332-0}{108/\sqrt{200}}\\ =43.47\end{array}$

The P-value is the probability of obtain a value more extreme or equal to the standardized test statistic

  $P=P\left(Z>43.47\right)=1-P\left(Z<43.47\right)=1-1=0$

  $P<0.01\Rightarrow \text{Reject}{H}_0$

There is enough evidence to support the claim that the mean amount charged increases under the no-fee offer.