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 90% level of confidence. For a sample of 837 third graders, the mean words per minute read was 24.9. Assume a population standard deviation of 5.1. Construct the confidence interval for the mean number of words a third grader can read per minute. Round your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 24.9

Population standard deviation =    = 5.1

Sample size = n = 837

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2 * ( /n)

= 1.645 * (5.1 /  837 )

= 0.3

At 90% confidence interval estimate of the population mean is,

  ± E

24.9 ± 0.3   

( 24.6, 25.2 )