Question

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 98%98% level of confidence. For a sample of 508508 third graders, the mean words per minute read was 29.829.8. Assume a population standard deviation of 3.23.2. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place.

Lower endpoint: ______ Upper endpoint:_____

Answer 1

Sample size = n = 508

Sample mean = = 29.8

Population standard deviation = = 3.2

We have to construct 98% confidence interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 2.32    ( Using z table)

So confidence interval is ( 29.8 - 0.3294 , 29.8 + 0.3294) = > ( 29.5 , 30.1)

Lower endpoint: 29.5

Upper endpoint: 30.1