Determining the Appropriate Sample Size SAMPLE SIZE REQUIREMENT - ESTIMATING  WITH  KNOWN where: z = Critical value for the specified confidence interval e = Desired margin of error  = Population standard deviation

Pilot Samples A pilot sample is a smaller sample taken from the population that is used to provide an estimate for the population standard deviation.

Example of Determining Required Sample Size (Example 7-7) The manager of the Georgia Timber Mill wishes to construct a 90% confidence interval with a margin of error of 0.50 inches in estimating the mean diameter of logs. A pilot sample of 100 logs yield a sample standard deviation of 4.8 inches.

Estimating A Population Proportion SAMPLE PROPORTION where: x = Number of occurrences n = Sample size

Estimating a Population Proportion STANDARD ERROR FOR p where:  =Population proportion n = Sample size

Confidence Interval Estimates for Proportions CONFIDENCE INTERVAL FOR  where: p = Sample proportion n = Sample size z = Critical value from the standard normal distribution

Example of Confidence Interval for Proportion (Example 7-8) 62 out of a sample of 100 individuals who were surveyed by Quick-Lube returned within one month to have their oil changed. To find a 90% confidence interval for the true proportion of customers who actually returned: 0.54 0.70

Determining the Required Sample Size MARGIN OF ERROR FOR ESTIMATING  where:  = Population proportion z = Critical values from standard normal distribution n = Sample size

Determining the Required Sample Size SAMPLE SIZE FOR ESTIMATING  where:  = Value used to represent the population proportion e = Desired margin of error z = Critical value from the standard normal table