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1 Chapter 10 Pssst! Coffee helps! Sample Size for an Interval Estimate of a Population Proportion Let E = the maximum sampling error mentioned in the precision statement. We have Solving for n we have Example: Political Science, Inc. Suppose that PSI would like a.99 probability that the sample proportion is within +.03 of the population proportion. A similar study performed on the same candidate in the same region resulted in a sample proportion of 44%. How large a sample size is needed to meet the required precision? 1
2 Example: Political Science, Inc. Three rules for estimating a Population Proportion 1. Use p from another similar study. 2. If no estimate of p is available, set p to Use from a pilot study, let Sample Size for Interval Estimate of a Population Proportion At 99% confidence, z.005 = Note,.44 is the best estimate of p in the above expression. If no information is available about p, what would you recommended as the size of n? In class exercise Kearney 6 th Graders Each member of a random sample of 25 sixth-graders in Kearney keeps a record for one week of the amount of time spent watching television. The sample mean and sample standard deviation computed from the results are 15 hours and 6 hours respectively. Construct a 95% confidence interval estimate for the population mean. Assume that the the time students spend watching television is normally distributed. Chapter 10 Statistical Inference - Two Populations Estimation of the Difference between the Means of Two Populations, Large Sample Independent Samples Population variances are unknown and unequal 2
3 Interval Estimate for the difference between two population means large sample, n>30 Where Interval Estimate For example Example Difference of Two Means At Carter Ironworks, two machines are used to produce metal rods. A random sample of 49 rods from Machine 2 and a random sample of 36 rods from Machine 1 give these results with respect to the lengths of metal rods produced. Construct the 95% confidence interval estimate for Carter Ironworks is 95% confident that the average length of rods from machine #1 is 0.04 to 0.16 feet longer that rods from machine #2. Two Population Proportions Estimation of the Difference between the Means of Two Proportions, Large Sample Independent Sample 3
4 Interval Estimate for the difference between two population proportions large sample Where Interval Estimate For example Example Difference of Two Proportions Political Science, Inc. (PSI) performed a telephone survey asking registered voters who they would vote for if the election were held that day. PSI found that 384 registered voters, out of 800 contacted, favored a particular candidate. The previous week showed 220 out of 500 voters favored the candidate. PSI wants to develop a 80% confidence interval estimate for the change in proportion of all registered voters that favors the candidate.` Current Previous Week We are 80% confident that the candidate s approval increased between.4% and 7.6%. 4
5 In class exercise Each member of a random sample of 50 sixth-graders in Kearney kept a record for one week of the amount of time spent watching television. The sample mean and sample variance are 15 hours and 10 hours 2. A second random sample of 40 second-graders in the Greenhill school district also kept records for one week of the amount of time spent watching television. The sample mean and sample variance are 10 hours and 5 hours 2. Construct a 95% confidence interval for the mean difference between Kearney 6 th graders and Greenhill 2 nd graders. Kearney & Greenhill Kearney 6 th graders Greenhill 2 nd graders In class exercise A Gallup poll found that 16% of 505 men and 25% of 496 women surveyed favored a law forbidding the sale of all beer, wine, and liquor throughout the nation. Develop a 95% confidence interval for the difference between the proportion of women who favor such a ban and the proportion of men who favor such a ban. 5
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