A psychologist is interested in the mean IQ score of a given group of children.

Question

A psychologist is interested in the mean IQ score of a given group of children. It is known that the IQ scores of the group have a standard deviation of 14. The psychologist randomly selects 150 children from this group and finds that their mean IQ score is 107. Based on this sample, find a 90% confidence interval for the true mean IQ score for all children of this group. Then complete the table below Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval? 105.119 What is the upper limit of the 90% confidence interval?

Explanation / Answer

Solution:- mean = 107 , sd = 14 , n = 150 , Z(0.05) = 1.645

90% confidence interval = X +/- Z*(sd/sqrt(n))

= 107+/-(1.645*(14/sqrt(150)))

= (107-(1.645*(14/sqrt(150))) , 107+(1.645*(14/sqrt(150))) )

= (105.1196 , 108.8804)

= (105.1 , 108.9) rounded.

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