Question

Recall the example: We wish to know whether children who grow up without access to a smartphone have higher IQs than children in the general population. IQ is normally distributed in the general population, with μ = 100 and σ = 15 points. Suppose we draw a random sample of n = 36 children without access to a smartphone and measure each child’s IQ. The mean IQ for our sample turns out to be 103.25. Construct a 95% confidence interval. Round answers to two decimal places.

What is the lower bound of the 95% CI?

What is the upper bound of the 95% CI?

Answer 1

Given  IQ is normally distributed in the general population, with μ = 100 and σ = 15 points. We draw a random sample of n = 36 children without access to a smartphone and measure each child’s IQ

The confidence interval for true mean based on the sample mean is

Here . 95% CI for mean is

the lower bound of the 95% CI is

the upper bound of the 95% CI is