Question

In a random sample of 7 residents of the state of Montana, the mean waste recycled...

In a random sample of 7 residents of the state of Montana, the mean waste recycled per person per day was 1.1 pounds with a standard deviation of 0.64 pounds. Determine the 90% 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.

Solution :

Given that,

sample size = n = 7

Degrees of freedom = df = n - 1 = 7 - 1 = 6

t$\alpha$ /2,df = 1.943

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

= 1.943 * (0.64 / $\sqrt$ 7)

= 0.470

The 90% confidence interval estimate of the population mean is,

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

1.1 - 0.470 < $\mu$ < 1.1 + 0.470

0.630 < $\mu$ < 1.570

90% confidence interval for the mean : (0.630 , 1.570)

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