Question

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

X (overbar) = 22

s = 3.2

n = 13

What assumptions need to be made about this​ population?

The 99​% confidence interval for the population mean is from a lower limit of __ to an upper limit of __. (round to two decimal places as needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 22

sample standard deviation = s = 3.2

sample size = n = 13

Degrees of freedom = df = n - 1 = 13 - 1 = 12

The population follows the Student's t-distribution.

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t _{0.005, 12} = 3.055

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

= 3.055 * (3.2 / 13)

Margin of error = E = 2.71

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

  ± E  

= 22  ± 2.71

= (19.29, 24.71)

The 99​% confidence interval for the population mean is from a lower limit of 19.29 to an upper limit of 24.71.