Chapter 11.1, Problem 24E

a.

To determine

To explain: The reason of using two sample test procedure in the provided case.

Explanation of Solution

Given:

The figure is:

  

The numerical summary is:

  

Formula used:

The formula to compute the confidence interval is:

  $\left({\overline{x}}_1-{\overline{x}}_2\right)\pm t_{\alpha /2,df}\times \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$

Here following conditions are fulfilled:

1. Samples have been chosen randomly.
2. Normality assumption is also fulfilled because size of each of the samples is more than 30.
3. Samples have been chosen independently.

Thus, all the required conditions for two-sample t test are fulfilled here.

b.

To determine

To construct: The 95% confidence interval and interpret it.

Answer to Problem 24E

The confidence interval is (0.11968, 0.44832)

Explanation of Solution

Calculation:

Using the Ti-83 calculator, the confidence interval is computed as:

  

The required confidence interval is (0.11968, 0.44832).

Interpretation:

There is 95% probability that difference of population means is between 0.11968 and 0.44832.

c.

To determine

To check: If the above computed confidence interval gives sufficient evidence that reading is causing increase in English’s grades.

Answer to Problem 24E

No.

Explanation of Solution

The provided study is an observational study. So, many confounders may be present which do not provide sufficient evidence to conclude that evidence that reading is leading increase in English’s grades.