Question

A simple random sample of size n=40 is drawn from a population. The sample mean is found to be x=121.7 and the sample standard deviation is found to be s=13.3.

Construct a​ 99% confidence interval for the population mean.

The lower bound is

​ (Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 121.7

sample standard deviation = s = 13.3

sample size = n = 40

Degrees of freedom = df = n - 1 = 40 - 1 = 39

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

t_,df = t_0.01,39 = 2.426

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

= 2.426 * (13.3 / 40)

= 5.10

The 99% lower confidence level is,

- E

121.7 - 5.10

116.6

The lower bound is: 116.6