Question

Construct a​ 99% confidence interval to estimate the population mean using the data below.   

x over bar equals 25

s equals 3.5

n equals 23

N equals 180

The​ 99% confidence interval for the population mean is (____,____)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 25

sample standard deviation = s = 3.5

sample size = n = 23

N = 180

Degrees of freedom = df = n - 1 = 23 - 1 = 22

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,22 = 2.819

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

= 2.819 * ( 3.5/ 23)

Margin of error = E = 2.06

The 99% confidence interval estimate of the population mean is,

  ± E  

= 25 ± 2.06

= ( 22.94, 27.06 )