Aim: How do we find an appropriate sample size?

HW#10: Complete question on last slide

Quiz Friday

Sample Size

• Sample size determination is closely related to statistical estimation

• How large a sample is necessary to make an accurate estimate

• Depends on three things: 1. the maximum error of estimate2. the population standard deviation3. the degree of confidence

Sample Size (n)

• Formula for minimum sample size needed for an interval estimate of the population mean

• Where E is the maximum error of estimate. • If necessary round the answer up to obtain a

whole number for sample size n.

2

2z

nE

Example

• The college president asks the statistic teacher to estimate the average age of the students at their college. How large a sample is necessary? The statistic teacher would like to be 99% confident that he estimate should be accurate within 1 year. From a previous study, the standard deviation of the ages is known to be 3 years.

Example Solution

• Since z=2.58 and E=1, substitute values in formula:

2 2

22.58 3

1

zn

E

Sample Size

• When finding the sample size, the size of the population is irrelevant when the population is large or infinite or when sampling is done with replacement

Class Work

• Complete Worksheet Handed Out Today • MUST hand into me at the end of the period.

HW#10: Making Decisions with Confidence Intervals

• Assume you work for Kimberly Clark Corporation, the makers of Kleenex. The job you are presently working on requires you to decide how many Kleenexes are to be put in the new automobile glove compartment boxes. Complete the following.

1. How will you deicide on a reasonable number of Kleenexes to put in the boxes?

2. When do people usually need Kleenexes?3. What type of data collection technique would you use? 4. Assume you found out that from your sample of 85 people on

average about 57 Kleenexes are used throughout the duration of a a cold, with a standard deviation of 15. Use a confidence interval to help you decide how many Kleenexes will go in the boxes. (use 95% confidence interval)

5. Explain how you decided on how many Kleenexes will go in the boxes.