Question

The following measurements (in picocuries per liter) were recorded by a set of argon gas detectors installed in a research facility: 203.6,185.9,199,178.7 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. Round your answer to two decimal places.

Answer 1

First we need to find the mean and standard deviation of sample. Following table shows the calcuations:

	X	(X-mean)^2
	203.6	139.24
	185.9	34.81
	199	51.84
	178.7	171.61
Total	767.2	397.5

Sample size: n=4

The standard deviation is:

$s=\sqrt{\frac{\sum \left ( x-\bar{x} \right )^{2}}{n-1}}=11.5109$

The degree of freedom: df=n-1=3

The critical value for 95% confidence interval is: 3.182

The confidence interval is:

191,.31-(073 1,210.11 11.5109 criticalE- 191.8±3.182 191.8±18.31 = (173.49.210.11)