(a)
Find the 85% confidence interval for
(a)

Answer to Problem 25P
The 85% confidence interval for
Explanation of Solution
Confidence interval:
The confidence interval for
In the formula,
Let
The confidence level is 85%.
Critical value:
Substitute 15 for
The degrees of freedom are 14.
Use the Appendix II: Tables, Table 6: Critical Values for Student’s t Distribution:
- In d.f. column locate the value 14.
- In c row of locate the value 0.85.
- The intersecting value of row and columns is 1.523.
The critical value is 1.523.
Substitute 15 for
The margin of error E is 1.87.
Substitute 19.84 for
Hence, the 85% confidence interval for
(b)
Find the 85% confidence interval for
(b)

Answer to Problem 25P
The 85% confidence interval for
Explanation of Solution
From part (a), the critical value is 1.523.
Substitute 15 for
The margin of error E is 1.90.
Substitute 19.84 for
Hence, the 85% confidence interval for
(c)
Find the 85% confidence interval for
(c)

Answer to Problem 25P
The 85% confidence interval for
Explanation of Solution
From part (a), the critical value is 1.523.
Substitute 15 for
The margin of error E is 2.05.
Substitute 19.32 for
Hence, the 85% confidence interval for
(d)
Interpret the confidence intervals found in (a), (b), (c) in the context of the problem.
Explain the relationship between average differences in influence on self-esteem between competence and social acceptance.
Explain the relationship between average differences in influence on self-esteem between competence and attractiveness.
Explain the relationship between average differences in influence on self-esteem between social acceptance and attractiveness.
(d)

Explanation of Solution
From part (a), the confidence interval for
The 85% confidence interval calculated for difference of means
From part (b), the confidence interval for
The 85% confidence interval calculated for difference of means
From part (c), the confidence interval for
The 85% confidence interval calculated for difference of means
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