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 95% level of confidence. For a sample of 695 third graders, the mean words per minute read was 38.3. Assume a population standard deviation of 3.6. 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 =     = 38.3

Population standard deviation =     = 3.6

Sample size n =695

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z / 2   = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
=1.96 * (3.6 / 695 )

= 0.3
At 95% confidence interval estimate of the population mean
is,

- E <   < + E

38.3 - 0.3 <   < 38.3+ 0.3

38.0 <   < 38.6

( 38.0, 38.6 )