Question

an IQ test is designed so that the mean is 100 and the standard deviation is 17 for the population of normal adults. Find the sample size necessary to estimate the mean IQ scores of statistic student such that it could be 95% confidence that the sample mean is within 7 IQ points of the mean. Assume that the mean = 17 and determine the required sample size using technology. Then determine if this is a reasonable sample for a real world calculation

Answer 1

Answer :

given data :-

the standard deviation = 17

S = 17

Margin of error = 7

E = 7

confidence interval = 95%

= 95/100

C = 0.95

Now we need to find out the required sample size using technology

we know that

=> n = z(alpha/2)^2 S^2 / E^2)

where,

S = 17

E = 7

z(alpha/2) => alpha = 1-C

= 1-0.95

  alpha = 0.05

z(alpha/2) = 0.05/2

z(alpha/2) = 0.025

by using the z normal table technology

z(alpha/2) = 1.96

Let,

n = z(alpha/2)^2 S^2 / E^2)

=> n = (1.96² * 17²)/7²

=> n = (3.8416 * 289)/49

=> n = 1110.2224/49

=> n = 22.6576

rounding up the answer

n = 23

  the required sample size using technology is : 23