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Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: 114...

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 96% confidence interval. to

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Expert Solution

Confidence interval for population mean when population standard deviation is known

Given,

Population standard deviation : = 15

Sample size of SRS of all seventh-grade girls in the school district: n= 31

Sum of test scores of 31 seventh-grade girls in school district =

Sample mean of test scores of 31 seventh-grade girls in school district:

= Sum of test scores of 31 seventh-grade girls in school district / Sample size = 3281/31=105.8387

for 96% confidence level = (100-96)/100 = 0.04

/2 =0.02

Z/2 = Z0.02 = 2.0537

96% confidence interval estimate of the mean IQ score for all seventh-grade girls in the school district

96% confidence interval estimate of the mean IQ score for all seventh-grade girls in the school district= (100.3059,111.3715)

milcah answered 1 month ago
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