A company that manufactures exercise machines wanted to know the percentage of large companies that provides on-site health club facilities. A sample of 240 such companies showed that 96 of them provide such facilities on site.

Question

a. What is the point estimate of the percentage of all such companies that provide these facilities? Explain briefly the concept of the point estimate.

b. Construct a 97% confidence interval for the percentage of all such companies.

c. What is the margin of error for this estimate?

d. If the company wanted a narrower interval, name two things it could do.

e. Which is the better strategy and why?

f. What does it mean to have a 97% confidence in the interval?

Answer 1

p = 96/240 q = (240-96)/240

n =240

a. find p
b. Find the z-value for a 97% confidence interval. You will most likely have to find the tails which is 3%/2 or 1.5% or .015

c. The margin of error is the +/- value that you will add to the p that you found originally.

d. For a narrower interval, you can use a smaller confidence and/ or do something with the n. (Do you know what that is)

Most people misinterpret what 97% confidence really means...

If you had the same population and took the sample of the same size over and over and over again. Did the math and created many, many, many confidence intervals then 97% of those intervals that you created will contain the true population mean.

97% does not mean that you have a 97% chance that the p that you found is correct.