Question

In a random sample of 19 residence of the state of Tennessee, the main waste recycling per person per day was 1.3 pounds with a standard deviation of 0.91 pounds. Determine the 95% confidence interval for the main waste recycle per person per day for the population of Tennessee. Assume the population is approximately normal.

Step 1 of 2: Find a critical value that should be used in constructing the confidence interval. Round your answer three decimal places.

Answer 1

Solution :

Given that,

= 1.3

s = 0.91

n = 19

Degrees of freedom = df = n - 1 = 19- 1 = 18

critical value of t is

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

critical value t _/2,df = t_0.025,18 =2.100

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

= 2.100 * (0.91 / 19) = 0.438 (rounded)

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

- E < < + E

1.3 - 0.438 < < 1.3 + 0.438

0.862 < < 1.738

(0.862, 1.738)