Exercise 4.16 describes a study on gifted children. In this study, along with variables on the children, the researchers also collected data on the mother's and father's IQ of the 36 randomly sampled gifted children. The histogram below shows the distribution of mother's IQ. Also provided are some sample statistics.

(a) Perform a hypothesis test to evaluate if these data provide convincing evidence that the average IQ of mothers of gifted children is different than the average IQ for the population at large, which is 100 . Use a significance level of 0.10.

(b) Calculate a \(90 \%\) confidence interval for the average IQ of mothers of gifted children.

(c) Do your results from the hypothesis test and the confidence interval agree? Explain.

Data From Exercise 4.16

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12 8 0 100 105 110 115 120 125 130 135 Mother's IQ n 36 min 101 mean 118.2 sd 6.5 max 131