Chapter 8, Problem 5CRE

a.

To determine

To define: The parameter µ involved in the setting.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample mean}\left(\overline{x}\right)=114.98\\ \text{Sample standard deviation}\left(s\right)=14.80\\ \text{Sample size}\left(n\right)=60\end{array}$

Formula used:

The formula of confidence interval is:

  $\overline{x}-t_{\alpha /2}\times \frac{s}{\sqrt{n}}<\mu <\overline{x}+t_{\alpha /2}\times \frac{s}{\sqrt{n}}$

The parameter µ exhibits the population mean which shows the mean IQ score of all the students that are studying in school.

b.

To determine

To explain: The reason of normality condition being satisfied here.

Answer to Problem 5CRE

Because the sample size is above 30.

Explanation of Solution

For the normality condition to be fulfilled the size of the sample should be above 30. Here, sample size is is 60 which is greater than 30. Thus, the condition of normalityt is fulfilled here.

c.

To determine

To construct: The 90% confidence interval

Answer to Problem 5CRE

The confidence interval is (111.79, 118.17)

Explanation of Solution

Calculation:

The obtained confidence interval using Ti-83 calculator is:

  

Thus, the confidence interval is (111.79, 118.17)

d.

To determine

To interpret: The confidence interval.

Explanation of Solution

There is 90% surity that the true mean IQ score of the students would fall between the 111.79 and 118.17.