Question

In a random sample of 39 residents of the state of Florida, the mean waste recycled per person per day was 2.1 pounds with a standard deviation of 0.87 pounds. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Florida. Assume the population is normally distributed. Step 2 of 2 : Construct the 95% confidence interval. Round your answer to one decimal place.

Answer 1

Solution :

Given that,

= 2.1

s = 0.87

n = 39

Degrees of freedom = df = n - 1 = 39 - 1 = 38

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,38 = 2.024

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

= 2.024 * (0.87 / 39)

= 0.28

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

- E < < + E

2.1 - 0.28 < < 2.1 - 0.28

1.82 < < 2.38

(1.8, 2.4)