Question

We wish to give a 95% confidence interval for the mean time it takes to complete a routine assembly task. To this end we obtain a random sample of 100 assembly times. We obtain a sample mean value of 15 minutes with a sample standard deviation of 5 minutes. Give the point estimate of the population average assembly time

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 15

sample standard deviation = s = 5

sample size = n = 100

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

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,99 = 1.984

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

= 1.984 * (5 / 100)

Margin of error = E = 0.9

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

- E < < + E

15 - 0.9 < < 15 + 0.9

14.1 < < 15.9

(14.1 , 15.9)