Question

A simple random sample of 23 third-grade children from a certain school district is selected, and each is given a test to measure his/her reading ability. You are interested in calculating a 90% confidence interval for the population mean score. In the sample, the mean score is 64 points and the standard deviation is 14 points. What is the margin of error associated with the confidence interval?

Answer 1

b )Given that,

= 64

s =14

n = 23

Degrees of freedom = df = n - 1 =23 - 1 = 22

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,22 = 1.717    ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 1.717* (14 / 23) = 5.01