Question

An article reported that for a sample of 40 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 163.36.

(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.

( ), ( ) ppm

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 654.16

sample standard deviation = s = 163.36

sample size = n = 40

Degrees of freedom = df = n - 1 = 39

t _/2,df = 2.023

Margin of error = E = t_/2,df * (s /n)

= 2.023 * (163.36 / 40)

Margin of error = E = 52.25

The 95% confidence interval estimate of the population mean is,

- E < < + E

654.16 - 52.25 < < 654.16 + 52.25

601.91 < < 706.41

(601.91 , 706.41) ppm