Question

A group of researchers was investigating the effect of early childhood intervention on the IQ tested later on in the upper elementary grades. A well-known IQ test with a mean of 100 was used to assess intelligence. A group of 40 ten year-olds from an economically disadvantaged area of a Midwestern city was given this IQ test, and a mean of 82 with a sample SD of 16 was obtained.

a. What is the 95% confidence interval for the study described above? (submit all work)

b. Provide an interpretation of your answer to part A.

c. Does the known population mean of 100 fall within the interval?

d. Provide an interpretation of your answer to part C.

Answer 1

Solution:-a) The 95% confidence interval for the study is C.I = ( 76.882, 87.118)

C.I = 82 + 2.023 × 2.529822

C.I = 82 + 5.1178

C.I = ( 76.882, 87.118)

b)  If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean.

c) Known population mean of 100 does not fall within the interval ( 76.882, 87.118).

d) We have sufficient evidence in the favor of the claim that population mean is less than 100.