Question

A simple random sample of size n is drawn. The sample​ mean, x is found to be 19.3 and the sample standard​ deviation, s, is found to be 4.7

a. Construct a 95% confidence interval about mu if the sample​ size, n, is 35

Answer 1

solution

Given that,

= 19.3

s =4.7

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* ( 4.7/ 35) = 1.6143

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

- E < < + E

19.3 - 1.6143 < < 19.3+ 1.6143

17.6857 < < 20.9143

( 17.6857 ,20.9143)