Confidence Interval

Confidence Interval estimate of population mean, known

A manufacturer of computer paper has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches and standard deviation is known to be .02 inch. At periodic intervals, samples are selected to determine whether the mean paper length is equal to 11 inches or whether something has gone wrong in the production process to change the length of the paper produced. If such a situation has occurred, corrective action is needed. Suppose a random sample of 100 sheets is selected, the mean paper length is found to be 10.998 inches. Set up a 95% confidence interval the population mean paper length.

Assumption: 1) population is normally distributed

2) sample is small and is unknown

If we use sample standard deviation s to replace

The statistic t follows distribution, which is called t-distribution.

Where s is sample standard deviation

ns

xt

/

1

)( 2

n

xx

s ixi

Confidence Interval estimate of population mean, unknown

Property of t-distribution

1) t-distribution is bell-shaped

2) t-distribution is perfectly symmetric about t=0

3) t-distribution is more variable than z

4) t-distribution is affected by the sample size n

Problem

A major pharmaceutical company has randomly sampled 14 customers who have used one of their new painkilling drugs for two months. There is concern that the drug may elevate the user’s heart rate. Each of the customers in the sample had their heart rate measured after using the drug for one week. All people had heart rates of 55 prior to taking drugs. The following data were recorded for the 14 customers.

50 70 60 70 90 72 50 80 85 55 66 70 80 40

• Suppose that you have just started working in the marketing department of the pharmaceutical company. You are asked to find out the interval estimate true mean heart rate at 95% confidence interval.

• Was the concerned expressed justified?

Problem 3The classified-advertisement manager of Daily

Statesman newspaper believes that the portion of “apartment for Sale” ads that are placed in the paper that result in a rental within two weeks is .9 or higher. She would like to make this claim as part of paper’s promotion of its classified section. Before doing this he has selected a random sample of 100 “apartment for sale” ads. Out of these 80 has resulted positive. What she will do?

What is the interval estimate of true fraction of claims at 99% confidence interval?