Question

In a random sample of 11

11

residents of the state of California, the mean waste recycled per person per day was 2.8

2.8

pounds with a standard deviation of 0.37

0.37

pounds. Determine the 95%

95

%

confidence interval for the mean waste recycled per person per day for the population of California. 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,

= 2.8

s =0.37

n = 11

Degrees of freedom = df = n - 1 = 11- 1 = 10

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_0.025,10 = 2.228

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

=2.228 * ( 0.37/ 11)

=0.249

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

- E < < + E

2.8 - 0.249 < < 2.8+ 0.249

2.551< < 3.049

( 2.551 , 3.049)