Question

Assuming the sample size is 30, the sample mean (X ̅) is 24.75, the sample standard deviation (s) is 5, and degrees of freedom are 29, a 95% confidence interval for the population mean would have lower bound of _________________ and upper bound of _______________________

Answer 1

Solution :

Given that,

= 24.75

s =5

n =30

Degrees of freedom = df = n - 1 =30 - 1 = 29

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,29 = 2.045 ( using student t table)

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

= 2.045* ( 5/ 30)

= 1.87

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

- E < < + E

24.75 - 1.87 < < 24.75 +1.87

22.88 < < 26.62

lower bound of ________22.88_________ and upper bound of ___________26.62____________