1. Business Statistics - QBM117 Selecting the sample size

2. Objectives w To determine an appropriate sample size for estimating a population mean . w To determine an appropriate sample size for estimating a population proportion.

3. Selecting the sample size w We have discussed on a number of occasions how important sample size is to the estimation of a parameter. w Generally, the larger the sample size, the better the estimate. w However large sample sizes are expensive, so what we require is the smallest sample that will give us the information, as accurately as we need it.

4. Selecting the sample size w Interval estimates provide a useful method of estimating an unknown parameter. w However, if the interval is too wide, it may not be very useful. w One way to control the width of the interval is by determining the most appropriate sample size, which will at the same time, provide narrow intervals.

5. To do this, we must specify three things w The parameter to be estimated ie  or p; w The desired level of confidence; w The maximum error of estimation, ie the acceptable error bound B.

6. Determining the appropriate sample size for estimating a population mean,  To estimate  when  is known we use To estimate  within some specified bound B, the confidence interval would simply be

7. Rearranging this formula to make n the subject we get Therefore it follows that If  is unknown, we estimate  by s and use the same formula

8. Exercise 8.39 p275 Here we are estimating the population mean 

9. Determining the appropriate sample size for estimating a population proportion p The formula for finding the sample size needed when we are estimating a population proportion is found in a similar way ie by solving the equation Rearranging this formula to make n the subject we get If we do not knowthe values of will provide the most conservative n are 0.5 and 0.5. which

10. Exercise 8.42 p275 Here we are estimating the population proportion p We have no idea of even approximate values of so we approximate them by 0.5 and 0.5 respectively.

11. Reading for next lecture Exercises to be completed before next lecture Revise chapter 8 S&S 8.39 8.41 8.43