Question

In a random sample of 5 residents of the state of Texas, the mean waste recycled per person per day was 1.9 pounds with a standard deviation of 0.89 pounds. Determine the 99% confidence interval for the mean waste recycled per person per day for the population of Texas. 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. Step 2 of 2 : Construct the 99% confidence interval. Round your answer to one decimal place.

Answer 1

solution

Given that,

=  1.9

s =0.89

n = 5

Degrees of freedom = df = n - 1 = 5- 1 = 4

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005, 4= 4.602    ( using student t table)

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

= 4.602 * (0.89 / 5) = 1.832

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

- E < < + E

1.9  - 1.832< < 1.9 + 1.832

0.068 < < 3.732

(0.07 , 3.7)