Chapter 9.3, Problem 91E

To determine

To perform: The complete analysis of the provided case using the provided output and draw the conclusion.

Explanation of Solution

Given:

The boxplot and output are:

  

Formula used:

The formula to compute the t-confidence interval for population mean is:

  $CI=\overline{x}\pm t_{\alpha /2,df}\times \frac{s}{\sqrt{n}}$

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =0\\ H_a:\mu \ne 0\end{array}$

From the provided output, the P -value is less than the significance level (0.05). Thus, the null hypothesis is rejected and it implies that there is enough evidence to agree with the provided claim at 5% significance level.

Here, the degree of freedom is:

  $\begin{array}{c}Df=n-1\\ =30-1\\ =29\end{array}$

The confidence interval using Ti-83 output is:

  

Thus, the 95% confidence interval is $\left(-1.561,-0.298\right)$

Since, the above computed confidence interval does not contain 0. There is enough evidence to agree with the provided claim.