Chapter 8.3, Problem 70E

a.

To determine

To find: The 95% confidence interval for the mean reading test score and interpret it.

Answer to Problem 70E

The confidence interval is (237.163, 242.837).

Explanation of Solution

Given:

Sample size ( n ) = 1470

Sample mean $\left(\overline{x}\right)=240$

Sample standard deviation $\left(s\right)=42.17$

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:

Here, t -confidence interval is to be used because population standard deviation is unknown.

The obtained excel output is:

  

Thus, the required confidence interval is (237.163, 242.837)

Interpretation:

There is 99% probability that the mean reading score lies between 237.163 and 242.837.

b.

To determine

To explain: Whether it could be concluded that the mean reading score is less than the basic level score, that is, 243

Answer to Problem 70E

Yes, it could be concluded the mean reading score is less than the basic level score.

Explanation of Solution

From the above, it is known that the confidence interval is (237.163, 242.837). Since, the mean reading score lies between 237.163 and 242.837. Thus, it could be concluded that the mean reading score is less than the basic level score