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.)

Question

Donna Cooley

Mathematics

12 April, 12:22

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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Isabelle French · 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)