Here are the IQ test scores of 31 seventh-grade girls in a Midwest school distri

Question

Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: 114 118 100 119 104 86 89 72 102 111 91 103 114 74 114 112 103 107 105 103 108 98 130 96 120 112 132 112 111 93 128 Suppose these 31 girls are random sample, and the standard deviation of IQ scores in this population is known to be 15. Construct a 95% confidence interval for the mean IQ score mu in the population. Show all the formulas and details. Use your calculator to check your work. Is there significant evidence at the 5% level that the mean IQ score in the population differs from 100? Show all the formulas and details to receive full credit. No credit for reporting results from a calculator directly.

Explanation / Answer

a) average, X=105.84

95% C.I ==>z=1.96

C.I = (105.84 - 1.96*15/sqrt(31) , 105.84 + 1.96*15/sqrt(31))

= (100.56 , 111.12)

b) z= (105.84-100)/(15/sqrt(31))=2.1677

The P-Value is 0.030182.

The result is significant at p < 0.05.

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