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Question: A sample of the reading scores of 35 sixth graders has a mean of 82. If the 95% confidence interval for the population mean of the reading scores of all fifth graders is between 77 and 87, then which among the following choices represents the 99% confidence interval?


A ) 74 < μ < 92
B ) 79 < μ < 85
C ) 77 < μ < 91
D ) 75 < μ < 89

Steps to derive

1 As the degree of confidence increases, the confidence interval becomes wider.

2 Choice 1: 77 - 74 < μ < 92 - 87
3 < μ < 5
The difference on both sides is not same.

3 Choice 2: 77 - 79 < μ < 85 - 87
- 2 < μ < - 2
The confidence interval should become wider not squeezed or compressed.

4 Choice 3: 77 - 77 < μ < 91 - 87
0 < μ < 4
The difference on both sides is not same.

5 Choice 4: 77 - 75 < μ < 89 - 87
2 < μ < 2
The difference on both sides is same and the confidence interval is wider than 95% confidence interval.

6 So, 75 < μ < 89 is the only choice that represents the 99% confidence interval.



Hence the right answer is Option D

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