Question

In a random sample of 14 residents of the state of Montana, the mean waste recycled per person per day was 1.4 pounds with a standard deviation of 0.71 pounds. Determine the 99% confidence interval for the mean waste recycled per person per day for the population of Montana. 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

Given that,

$\bar x$ = 1.4

s = 0.71

n = 14

Degrees of freedom = df = n - 1 = 14 - 1 = 13

At 99% confidence level the t is ,

$\alpha$ = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

critical value _{t$\alpha$ /2  df} = t_0.005,13 =3.012    ( using student t table)

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 3.012 * (0.71 / $\sqrt$ 14) = 0.57

The 99% confidence interval is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

1.4 - 0.57< $\mu$ < 1.4+ 0.57

0.83 < $\mu$ < 1.97

(0.83 , 1.97)