An article reported that for a sample of 52 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 164.55.

a) calculate and interpret a 95% confidence interval for true average CO2 level in the population of all homes from which the sample was selected .

b) Suppose the investigators had made a rough guess of 175 for the value of s before collecting data .What sanple size would be necessary to obtain an interval width of 50 ppm for confidence level of 95% ?

a)    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

b)

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that

Replacing we got:

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

Part b

The margin of error is given by :

   (a)

The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

  (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got , and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:

answer: f = 32.2m

step-by-step explanation: that is the answer