An article reported that for a sample of 55 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 162.34. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)

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Mathematics

Eden Banks

31 May, 18:28

An article reported that for a sample of 55 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 162.34. (a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)

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Dakota Nunez · Answer 1

Step-by-step explanation:

Given that

sample size n = 55: x bar = 654.16 and s = sample sd = 162.34

Std error = 162.34/sqrt 55 = 21.889

For 95% CI we can use t critical value as population std dev is not known.

df = 54

t critical = 2.004

Margin of error = 2.004 * 21.889 = 43.866

Confidence interval lower bound = 654.16-43.866 = 610.294

Upper bound = 654.16+43.866=698.026

Confidence interval rounded off at 95% = (610.29, 698.23)