Question

I WILL GIVE MEDAL AND FAN! A random sample of 125 students is chosen from a population of 4,000 students. If the mean IQ in the sample is 100 with a standard deviation of 8, what is the 98% confidence interval for the students' mean IQ score?

Answer 1

100−120

98.33−101.67

92−108

108.66−111.34

Answer 2

@kirbykirby

Answer 3

You will need to use:
\[\large \left(\bar{x} -z\frac{s}{\sqrt{n}},\bar{x}+z\frac{s}{\sqrt{n}}\right)\]
where \(\bar{x}\) is the mean, \(s\) is the standard deviation and \(z\) is the critical z value. We can use a \(z\)-value since your sample is large (\(\ge 30\)). Since a confidence interval of 98% means there is 1% on each side of the distribution. SO you will need to look a the standard normal distribution at a 0.99, which is about 2.33

Answer 4

All you need to do is substitute the values you are given and noticing that \(n\) is the number of students in the sample (not in the population).