Question

In a random sample of 23 residents of the state of Tennessee, the mean waste recycled per person per day was 2.1 pounds with a standard deviation of 0.9 pounds. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Tennessee. Assume the population is approximately normal.

Step 1 of 2 :  

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Solution :

Given that,

= 2.1

s = 0.9

n = 23

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

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,22 =2.074

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

= 2.074 * (0.9/ 23) = 0.3892

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

- E < < + E

2.1 - 0.3892 < < 2.1+ 0.3892

1.7108 < < 2.4892

(1.7108, 2.4892 )