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 165.4. Required:
a. Calculate and interpret a 9596 (two-sided) confidence interval for true average C02 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 sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%?

a)    

b)

So the answer for this case would be n=189 rounded up to the nearest integer

Step-by-step explanation:

Part a

represent the sample mean

population mean (variable of interest)

s=165.4 represent the sample standard deviation

n =52represent the sample size  

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

  (1)

The degrees of freedom aregiven by:

Since the Confidence is 0.95 or 95%, the significance and , and the critical value would be

Now we have everything in order to replace into formula (1):

Part b

The margin of error is given by this formula:

   (a)

And on this case we have that ME =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 this case wuld be , replacing into formula (b) we got:

So the answer for this case would be n=189 rounded up to the nearest integer