Question

The following measurements (in picocuries per liter) were recorded by a set of carbon dioxide detectors installed in a manufacturing facility:
828.1,812.1,805.9,810,831.3 1. 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.
2. Find the critical value that should be used in constructing the confidence interval.

Answer 1

The confidence interval for the mean level of carbon dioxide present in the facility is (806.05,828.91) and the critical value is 2.77 which is used to find out the confidence interval.

Given measurement of carbon dioxide :828.1,812.1,805.9,810,831.3

We have to construct a confidence interval for 95% for the mean level of carbon dioxide present in the facility.

n=5

sample mean=817.48 (calculated in figure)

sample standard deviation=$\sqrt{(x_ -x_{bar} )^{2} /n-1 }$

=$\sqrt{522.768/4}$

=11.43

We have to apply t test as n<30

t critical at 95% with degree of freedom=4              (5-1)

=2.77

Confidence interval=X bar ±standard error

Standard error= t*s/$\sqrt{n}$

=2.77*11.43/$\sqrt{5}$

=14.13

Lower boundary=817.48-11.43

=806.05

Upper boundary=817.48+11.43

=828.91

Hence the confidence interval is (806.05,828.91).

Learn more about confidence interval at brainly.com/question/15712887

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