Question

1) If n= 27, x bar=38, and s=10, find the margin of error at a 90% confidence level. Give your answer to two decimal places.

2) Express the confidence interval (14.4%, 24.2%) in the form of ˆp ± M E.

Answer 1

Solution :

Given that,

= 38

s = 10

n = 27

Degrees of freedom = df = n - 1 = 27 - 1 = 26

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,26 =1.706

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

= 1.706 * (10 / 27) = 3.2832

The 90% confidence interval estimate of the population mean is,

- E < < + E

38 - 3.2832< < 38 + 3.2832

34.72 < < 41.28

(34.72 ,  41.28)