Question

in a random sample of 6 residents of the state of maine, the mean waste recycled per person per day was 1.1 pounds with a standard deviation of 0.6 pounds. determine the 99 % confidence interval for the mean waste recycled per person per day for the population of maine. 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.

Explanation:

Step1: Identify distribution and parameters

We have a small sample (\(n = 6\)), population is approximately normal, and we know the sample standard deviation, so we use the t - distribution. The confidence level is \(99\%\), so the significance level \(\alpha=1 - 0.99 = 0.01\). The degrees of freedom \(df=n - 1=6 - 1 = 5\). We need to find the critical value \(t_{\alpha/2,df}\), where \(\alpha/2=\frac{0.01}{2}=0.005\) and \(df = 5\).

Step2: Find the t - critical value

Using a t - table or a calculator (such as the T.INV.2T function in Excel), for \(df = 5\) and \(\alpha = 0.01\) (two - tailed), the critical value \(t_{0.005,5}\) is approximately \(4.032\).

Answer:

\(4.032\)