Confidence Interval Question

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 16. The psychologist randomly selects 60 children from this group and finds that their mean IQ score is
99. 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.

 

What is the lower limit of the 90% confidence level?

What is the upper limit of the 90% confidence level?

 

Answer 1

The confidence interval = mean ± MOE where MOE = z critical (for 90%) * standard error where standard error  = standard deviation ÷ √sample size

 

standard error = 16 ÷ √60 = 2.06559

 

z critical (for 90%, found in a standard normal Z table) = 1.6449

 

MOE = 1.6449 *  2.06559 = 3.3977

 

Confidence Interval Lower Limit = Mean - MOE = 99 - 3.3977 = 95.602

 

Confidence Interval Upper Limit = Mean + MOE = 99 + 3.3977 = 102.40

 

Does this help?