Question

In a random sample of 8 residents of the state of Washington, the mean waste recycled per person per day was 1.9 pounds with a standard deviation of 0.29 pounds. Determine the 80% confidence interval for the mean waste recycled per person per day for the population of Washington. Assume the population is approximately normal. Step 2 of 2: Construct the 80% confidence interval. Round your answer to one decimal place. Lower end__________ Upper end______________

Answer 1

Solution :

Given that,

= 1.9

s = 0.29

n = 8

Degrees of freedom = df = n - 1 = 8 - 1 = 7

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

t _/2,df = t_0.10,7 = 1.415

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

= 1.415 * (0.29 / 8)

= 0.1

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

- E < < + E

1.9 - 0.1< < 1.9 + 0.1

1.8 < < 2.0

Lower end = 1.8

Upper end = 2.0

(,)