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 12. The psychologist randomly selects 150 children from this group and finds that their mean IQ score is 103. Based on this sample find a 99% 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 99% confidence interval? What is the upper limit of the 99% confidence interval?

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =12/(150)1/2 =0.98

for 99% confidence interval ; critical value of z=2.5758

therefore lower limit of 99% confidence interval = sample mean -/+ z*std error =103-2.5758*0.98 =100.5

upper limit of 99% confidence interval = sample mean -/+ z*std error =103+2.5758*0.98 =105.5

please revert for any clarification required.

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