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 80%80% level of confidence. For a sample of 600600 third graders, the mean words per minute read was 39.839.8. Assume a population standard deviation of 4.74.7. 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 =     =39.8

Population standard deviation =    = 4.7

Sample size n =600

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z/2 = Z0.10 = 1.28 ( Using z table )

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

= 1.28 * (4.7 / 600 )

E= 0.25
At 80% confidence interval estimate of the population mean
is,

- E < < + E

39.8 - 0.25 <   < 39.8 + 0.25

39.55 <   < 40.05

( 39.6 , 40.1 )