Question

A random sample of 145 students is chosen from a population of 4,250 students. If the mean IQ in the sample is 130 with a standard deviation of 7, what is the 90% confidence interval for the students' mean IQ score?

Answer 1

Confidence interval is given by the formula

x ⁺/₋ z* ( σ/ (√n) )

Where:

x = the sample mean = 130
z* = the z-value for 90% confidence = 1.645
σ = standard deviaton = 7
n = sample size = 145

Substituting these values into the formula gives:

130 ⁺/₋
`1.645( (7)/( √(145) ))`
130 ⁺/₋ 0.956

So the interval is in between (130 - 0.956) and (130 + 0.956)