Question

A group of 62 randomly selected students have a mean score of 28.3 on a standardized placement test. The population SD for all students taking the test is `sigma = 3.4`. What is the 90 percent confidence interval for the mean score?

Answer 1

Population mean is likely to fall between `29.005` and `27.595`

Explanation:

Given -

`barx=28.3`
`n=62`
`sigma=3.4`
`z` score for 90% confidence interval `1.64`
`SE=sigma/sqrtn=3.4/sqrt62=3.4/7.87=0.43`

90% confidence interval is defined by the formula

`mu=barx+(SExxz)` --------upper limit
`mu=28.3+(0.43 xx 1.64)=28.3+0.705=29.005`

`mu=barx-(SExxz)` --------Lower limit
`mu=28.3-(0.43 xx 1.64)=28.3-0.705=27.595`

Sample means are normally distributed around the population mean `mu`

An interval is developed as `29.005` and `27.595`. There is 90% chance for the population mean to fall in this interval.