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An article reported that for a sample of 58 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.)    ,     ppm Interpret the resulting interval. We are 95% confident that the true population mean lies below this interval.We are 95% confident that this interval does not contain the true population mean.    We are 95% confident that this interval contains the true population mean.We are 95% confident that the true population mean lies above this interval. (b) Suppose the investigators had made a rough guess of 172 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)  kitchens

An article reported that for a sample of 58 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.)    ,     ppm Interpret the resulting interval. We are 95% confident that the true population mean lies below this interval.We are 95% confident that this interval does not contain the true population mean.    We are 95% confident that this interval contains the true population mean.We are 95% confident that the true population mean lies above this interval. (b) Suppose the investigators had made a rough guess of 172 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)  kitchens

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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An article reported that for a sample of 58 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.)
 
  ,  
 
 ppm

Interpret the resulting interval.
We are 95% confident that the true population mean lies below this interval.We are 95% confident that this interval does not contain the true population mean.    We are 95% confident that this interval contains the true population mean.We are 95% confident that the true population mean lies above this interval.

(b) Suppose the investigators had made a rough guess of 172 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
 kitchens
Expert Solution
Step 1

Given that,

a)

Sample mean is

 x¯=654.16

The sample standard deviation is

s=162.34

Sample size

n=58

Confidence level

CI=0.95

The confidence interval for the population mean is as follows,

x¯-tcsn,x¯+tcsn

tc is t critical value with a level of significance and degrees of freedom

b) 

Sample standard deviation s=172

The width of the confidence interval is 50.

CI=0.95

The formula for the sample size is

n=ZcsE2

Zc is the z critical value

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