Question

Assume that we want to estimate the mean IQ score for the population of statistics students. How many students must be randomly selected for IQ tests if we want 90% confidence that the sample mean is within 4 IQ points of the population mean and the population standard deviation o = 15?

Answer 1

we have margin of error = 4

standard deviation = 15

we have to find sample size n for 90% confidence interval

so, we need to determine the value of z critical using z distribution for 90% confidence interval

we get, z = 1.64 (using z distribution table)

Formula for the sample size n is given as

where we have z = 1.64, ME(margin of error) = 4 and

setting the values, we get

Rounding it to nearest integer, we get

sample size n = 38

So, required number of students is 38