Question

In a random sample of 9 residents of the state of Florida, the mean waste recycled per person per day was 2.4 pounds with a standard deviation of 0.75 pounds. Determine the 80% confidence interval for the mean waste recycled per person per day for the population of Florida. 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,

= 2.4

s =0.75

n = 9

Degrees of freedom = df = n - 1 = 9- 1 = 8

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

  / 2= 0.20 / 2 = 0.10

t /2,df = t0.10, 8 = 1.397 ( using student t table)

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

=1.397 * (0.75 / 9)

E=0.3493

The 80% confidence interval estimate of the population mean is,

- E < < + E

2.4 - 0.3493 < < 2.4+ 0.3493

2.0507< < 2.7493

( 2.0507, 2.7493)