a)
To explain why it is acceptable to use two-sample t test.
a)
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
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 construct 95% confidence interval for difference in means.
b)
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 explain if the confidence interval provide evidence that reading more causes a difference in student’s English grades.
c)
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.
Chapter 11 Solutions
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