Question

A researcher is interested to determine the average number of years new teachers remain in the classroom. A pilot study of 385 teachers showed a sample standard deviation of 8 years and a mean of 12 years. What is the 95% confidence interval estimate of the mean time new teachers remain in the classroom? Round your answers to the nearest whole number.

A.10 to 13 years

B.6 to 12 years

C. 9 to 12 years

D. 11 to 13 years

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 12

sample standard deviation = s = 8

sample size = n = 385

Degrees of freedom = df = n - 1 = 385-1 = 384

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,384 = 1.966

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

= 1.966 * (8 / 385)

= 1

The 95% confidence interval estimate of the population mean is,

- E < < + E

12 - 1 < < 12 + 1

11 < < 13

(11,13), D) 11 to 13 years , Option D is correct.