Question

A researcher wanted to give a 60% confidence interval for the mean time it takes worker to perform a routine task. The researcher had a random sample of 100 worker perform the task. The sample mean time to perform the task was 21 minutes with a sample standard deviation of 2 minutes. Give the 60% confidence interval for the population mean time to perform the task. Round your answer to two decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 21

sample standard deviation = s = 2

sample size = n = 100

Degrees of freedom = df = n -1= 100-1=99  

At 60% confidence level the t is ,

= 1 - 60% = 1 - 0.6 = 0.4

/ 2 = 0.4/ 2 = 0.2

t /2,df = t0.2,99 = 0.845

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

= 0.845 * (2 / 100)

Margin of error = E = 0.17

The 60% confidence interval estimate of the population mean is,

- E < < + E

21 - 0.17 < < 21 + 0.17

20.83 < < 21.17

(20.83,21.17)