Question

The following measurements (in picocuries per liter) were recorded by a set of argon gas detectors installed in a research facility: 831.7, 847.2, 820.9, 826.3 Using these measurements, construct a 95% confidence interval for the mean level of argon gas present in the facility. Assume the population is approximately normal.

Step 1. Calculate the sample mean for the given sample data. Round your answer to two decimal places. Answer: ____________________

Step 2. Calculate the sample standard deviation for the given sample data. Round your answer to two decimal places. Answer: ____________________

Step 3. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. Answer: ____________________

Step 4. Construct the 95% confidence interval. Round your answer to two decimal places. Answer: Lower endpoint: _______________ Upper endpoint: _______________

Answer 1

sample mean, xbar = 831.53
sample standard deviation, s = 11.34
sample size, n = 4
degrees of freedom, df = n - 1 = 3

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 3.182

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (831.53 - 3.182 * 11.34/sqrt(4) , 831.53 + 3.182 * 11.34/sqrt(4))
CI = (813.49 , 849.57)