An article reported that for a sample of 45 kitchens with gas cooking appliances

Question

An article reported that for a sample of 45 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 163.7.

(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

(b) Suppose the investigators had made a rough guess of 171 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 59 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
___ kitchens

Explanation / Answer

here std error =std deviation/(n)1/2 =24.403

for 44 degree of freedom and 95% CI, t=2.015

a) hence confidence interval =sample mean -/+t*std error =604.98; 703.34

above interval provide 95% confidence to contain true population mean of CO2 level in the population of all homes from which the sample was selected

b) margin of error E=59/2=29.5

std deviation =171

for 95% CI, z=1.96

hence sample size n=(z*std deviation/E)2 =~130

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