Chapter 11.1, Problem 25E

a)

To determine

To explain why it is acceptable to use two-sample t test.

Answer to Problem 25E

All conditions satisfied so it is acceptable to use two-sample t test.

Explanation of Solution

Given:

The box plot:

Summary statistic:

Calculation:

Two sample t-test will be acceptable if and inly if their conditions will be satisfied.

The sample is random sample so, condition of random is satisfied.

The outliers in the box plot is mild and the sample size greater than 30 so, normal condition also satisfied.

The sample sizes 47 and 32 are both less than 10% of the population size so, independent condition also satisfied.

Therefore, it is acceptable to use two sample t-test.

b)

To determine

To construct 95% confidence interval for difference in means.

Answer to Problem 25E

The 95% confidence interval for the difference in the mean English grade for light and heavy readers is (0.1254, 0.4426)

Explanation of Solution

Given:

The box plot:

Summary statistic:

Calculation:

The excel output is,

Heavy	Light
3.64	3.356	mean
0.324	0.38	std. dev.
47	32	n
	77	df
	0.2840	difference (Heavy - Light)
	0.1208	pooled variance
	0.3476	pooled std. dev.
	0.0797	standard error of difference
	0.1254	confidence interval 95% lower
	0.4426	confidence interval 95% upper
	0.1586	margin of error

The 95% confidence interval for the difference in the mean English grade for light and heavy readers is (0.1254, 0.4426)

c)

To determine

To explain if the confidence interval provide evidence that reading more causes a difference in student’s English grades.

Answer to Problem 25E

There is enough evidence that reading more causes a difference in student’s English grades.

Explanation of Solution

Given:

The 95% confidence interval for the difference in the mean English grade for light and heavy readers is (0.1254, 0.4426)

Calculation:

The confidence interval does not contain zero. Therefore, there is enough evidence that reading more causes a difference in student’s English grades.