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 85% level of confidence. For a sample of 295 third graders, the mean words per minute read was 26.9. Assume a population standard deviation of 2.7. 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

85% level of the confidence interval is

(26.337, 26.662)

Explanation:

Explanation:-

Given the size of the sample 'n' = 295

Mean of the sample x⁻ = 26.5

The Standard deviation of the Population = 2.7

85% level of the confidence interval is determined by

`(x^(-) - Z_(0.15) (S.D)/(√(n) ) , x^(-) + Z_(0.15) (S.D)/(√(n) ))`

Critical value Z₀.₁₅ = 1.036

85% level of the confidence interval is determined by

`(x^(-) - Z_(0.15) (S.D)/(√(n) ) , x^(-) + Z_(0.15) (S.D)/(√(n) ))`

`(26.9 -1.036 (2.7)/(√(295) ) , 26.5 + 1.036 (2.7)/(√(295) ))`

( 26.5 - 0.1628 , 26.5+0.1628)

(26.3372,26.6628)