In: Statistics and Probability
A firm would like to know the average time its workers spend on a certain task. The firm takes a sample of 35 workers and finds that they take, on average, 13 minutes to complete the task, with a sample standard deviation of 3 minutes. Construct a 95% confidence interval for the population mean.
a) State the critical value:
b) Calculate the margin of error (round to the thousandths place):
c) State the lower and upper values of the confidence interval:
Solution :
Given that,
= 13
s =3
n =35
Degrees of freedom = df = n - 1 = 35- 1 = 34
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2= 0.05 / 2 = 0.025
t /2,df = t0.025,34 =2.032 ( using student t table)
Margin of error = E = t/2,df * (s /n)
= 2.032* ( 3/ 35)
= 1.0304
The 95% confidence interval estimate of the population mean is,
- E < < + E
13- 1.0304 < < 13+ 1.0304
11.9696 < < 14.0304
( 11.9696 , 14.0304 )