Wednesday

August 20, 2014

August 20, 2014

Posted by **Steven** on Sunday, March 10, 2013 at 5:12pm.

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?

- Statistics -
**Dr. Jane**, Sunday, March 10, 2013 at 6:20pmThe point estimate is an estimate of the population percentage given the sample you are working with.

Percentage = 96/240 = p-hat

q-hat = 1 - p-hat

97% confidence interval means that you have 3% left which is split between two tails. You need to split .03 in half to get .015. Find that value in the body of the z-table and use that value to get the z-score from the margins of the table.

You then calculate the margin of error using, p-hat, q-hat and n along with z. That answer is the number that you add or subtract to p- hat value to get the confidence interval.

To get a narrow interval, you can adjust the confidence interval.. ex. 95% gives you a narrower interval. You can also adjust the sample size.

People often confuse the meaning of a 97% confidence interval. It means that if you took many, many samples from the same population and found the percentage, calculated the confidence intervals in each case then 97% of those confidence intervals that you constructed will contain the true population percentage.

You cannot say that there is a 97% chance that this value will be within the 97% or that it represents the true population mean.

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