Question

The following measurements (in picocuries per liter) were recorded by a set of carbon dioxide detectors installed in a manufacturing facility: 799.2,784.3,803.8,806.8,780.5,794.8 Using these measurements, construct a 95% confidence interval for the mean level of carbon dioxide present in the facility. Assume the population is approximately normal. Step 3 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

(783.806 ; 805.994)

Explanation:

Given the sample :

X : 799.2,784.3,803.8,806.8,780.5,794.8

Sample size, n = 6

Sample mean, xbar = Σx / n = 794.9

Sample standard deviation, s = 10.574 ( calculator)

Tcritical at 95%, df = 6 - 1 = 5 equals 2.57

Confidence interval :

Xbar ± standard error

Standard Error = Tcritical * s/√n

Standard error = 2.57 * 10.574/√6 = 11.094

Lower boundary = (794.9 - 11.094) = 783.806

Upper boundary = (794.9 + 11.094) = 805.994

(783.806 ; 805.994)