Question

1. Assume we want to estimate the mean IQ score for the population of statistics students. How many statistics students must be randomly selected for IQ tests if we want to be 99% confident that the sample mean is within 5 IQ points of the true population mean? Consider the population’s standard deviation = 15.

Answer 1

SOLUTION:

From given data,

Assume we want to estimate the mean IQ score for the population of statistics students. How many statistics students must be randomly selected for IQ tests if we want to be 99% confident that the sample mean is within 5 IQ points of the true population mean? Consider the population’s standard deviation = 15.

we have margin of error = ME = 5

standard deviation = = 15

we have to find sample size n for 99% confidence interval

so, we need to determine the value of z critical using z distribution for 99% confidence interval

99% confidence interval

Confidence interval is 99%

99% = 99/100 = 0.99

= 1 - Confidence interval = 1-0.99 = 0.01

/2 = 0.01 / 2

= 0.005

Z_/2 = Z_0.005  = 2.58  (using z distribution table)

Formula for the sample size n is given as

n= ((Z_/2*) / ME)²

where we have z = 2.58, ME(margin of error) = 5 and =15

setting the values, we get

n= ((1.64*15)/5)^2

= 4.92^2 = 24.2064

Rounding it to nearest integer, we get

sample size n = 24

So, required number of students is 24