An IQ tests are designed to produce test results that are normally distributed w

Question

An IQ tests are designed to produce test results that are normally distributed with a mean of 100 and a standard deviation of 15 of a population. A study was conducted to determine if the average IQ scores of children whose parents had been divorced (for more than 4 years) is less than that for other children. IQ tests were administered to a total of 36 children whose parents had been divorced for at least 4 years. a) How many children would need to be sampled to have a margin of error of plusminus or smaller in the 95% confidence interval? For this part of the problem, you can assume the true standard deviation, sigma, for children of divorced parents to actually be 15.0. b) The mean IQ score for this sample of 26 children was 95.7 with a standard deviation of 18.3. Calculate the 95% confidence interval for the mean IQ of all children of divorced parent (for 4 years). c) Based on your answer in part (b), it is reasonable to assume that true population mean IQ score of children from divorced parents (for 4 years) is different than the general population (the true average IQ is 100 in the general population)? How do you know?

Explanation / Answer

here magin of error E =2

and std deviation =15

for 95% CIO, z=1.96

hence sample size =(z*std deviation/E)2 =217

b)here std error=std deviation/(n)1/2 =3.5889

hence confidence interval =mean -/+ z*std error =88.6658 ; 102.7342

c)as out confidence interval contains 100 as probable mean value we can not reject that it is differnt from general population

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