Question

In a random sample of 5 residents of the state of Maine, the mean waste recycled per person per day was 2.6 pounds with a standard deviation of 0.69 pounds. Determine the 98% 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.

Answer 1

(1.307 ; 3.893)

Explanation:

Given that:

Mean, xbar = 2.6

Standard deviation, s = 0.69

Sample size, n = 5

Confidence interval : xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Degree of freedom (df) = n - 1 = 5 - 1 = 4

Hence Tcritical = 3.747

Margin of Error = 3.747 * 0.69/sqrt(4)

Margin of Error = 1.293

Lower boundary = (2.6 - 1.293) = 1.307

Upper boundary = (2.6 + 1.293) = 3.893

(1.307 ; 3.893)