SOLUTION: Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: 114 100 104 89 102 91 114 114 103 105 108 130 120 132 11

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Question 866626: Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:
114 100 104 89 102 91 114 114 103 105
108 130 120 132 111 128 118 119 86 72
111 103 74 112 107 103 98 96 112 112 93

These 31 girls are an SRS of all seventh-grade girls in the school district.
Suppose that the standard deviation of IQ scores in this population is known to be σ = 15. We expect the distribution of IQ scores to be close to Normal.
Estimate the mean IQ score for all seventh-grade girls in the school district, using a 98% confidence interval.
Question 2 options:

105.84 to 132.00

72.00 to 132.00

100.56 to 111.12

99.57 to 112.11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First find the sample mean. You do so by adding up all the numbers and dividing by 31 (since there are 31 numbers).


Add up all the numbers to get 3281. Divide this by 31 to get 3281/31 = 105.8387


The sample mean is usually denoted xbar, so xbar = 105.8387 (this is approximate)

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Now we turn to this table. Look in the row that starts with infinity and look above the 98%. The value you'll see in this spot is 2.326


The critical value is z = 2.326


This is the critical value for the 98% confidence interval.
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To sum things up, we found the following


xbar = 105.8387 (sample mean)
z = 2.326 (critical value for the 98% confidence interval)


values above are approximate


The values given to us were

n = 31 (sample size)
σ = 15 (population standard deviation)

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We can finally compute the lower bound L and the upper bound U of the confidence interval


L = xbar - z*σ/sqrt(n)
L = 105.8387 - 2.326*15/sqrt(31)
L = 99.57227
L = 99.57 rounding to 2 decimal places


U = xbar + z*σ/sqrt(n)
U = 105.8387 + 2.326*15/sqrt(31)
U = 112.1051
U = 112.11 rounding to 2 decimal places


The confidence interval [L,U] or (L,U) is approximately [99.57, 112.11] or (99.57, 112.11)


So the answer is 99.57 to 112.11 which is choice D