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Pendugaan Parameter Proposi dan Beda Beda Proporsi Pertemuan 17

Pendugaan Parameter Proposi dan Beda Beda Proporsi Pertemuan 17. Matakuliah : I0134/Metode Statistika Tahun : 2007. Interval Estimation of a Population Proportion. Interval Estimate where: 1 -  is the confidence coefficient z  /2 is the z value providing an area of

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Pendugaan Parameter Proposi dan Beda Beda Proporsi Pertemuan 17

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  1. Pendugaan Parameter Proposi dan Beda Beda ProporsiPertemuan 17 Matakuliah : I0134/Metode Statistika Tahun : 2007

  2. Interval Estimationof a Population Proportion • Interval Estimate where: 1 - is the confidence coefficient z/2 is the z value providing an area of /2 in the upper tail of the standard normal probability distribution is the sample proportion

  3. Example: Political Science, Inc. • Interval Estimation of a Population Proportion Political Science, Inc. (PSI) specializes in voter polls and surveys designed to keep political office seekers informed of their position in a race. Using telephone surveys, interviewers ask registered voters who they would vote for if the election were held that day. In a recent election campaign, PSI found that 220 registered voters, out of 500 contacted, favored a particular candidate. PSI wants to develop a 95% confidence interval estimate for the proportion of the population of registered voters that favors the candidate.

  4. Example: Political Science, Inc. • Interval Estimate of a Population Proportion where: n = 500, = 220/500 = .44, z/2 = 1.96 .44 + .0435 PSI is 95% confident that the proportion of all voters that favors the candidate is between .3965 and .4835.

  5. Sample Size for an Interval Estimateof a Population Proportion • Let E = the maximum sampling error mentioned in the precision statement. • We have • Solving for n we have

  6. Example: Political Science, Inc. • Sample Size for an Interval Estimate of a Population Proportion Suppose that PSI would like a .99 probability that the sample proportion is within + .03 of the population proportion. How large a sample size is needed to meet the required precision?

  7. Example: Political Science, Inc. • Sample Size for Interval Estimate of a Population Proportion At 99% confidence, z.005 = 2.576. Note: We used .44 as the best estimate of p in the above expression. If no information is available about p, then .5 is often assumed because it provides the highest possible sample size. If we had used p = .5, the recommended n would have been 1843.

  8. Estimating the Difference between Two Proportions • Sometimes we are interested in comparing the proportion of “successes” in two binomial populations. • The germination rates of untreated seeds and seeds treated with a fungicide. • The proportion of male and female voters who favor a particular candidate for governor. • To make this comparison,

  9. Estimating the Difference between Two Means • We compare the two proportions by making inferences about p1-p2, the difference in the two population proportions. • If the two population proportions are the same, then p1-p2 = 0. • The best estimate of p1-p2is the difference in the two sample proportions,

  10. The Sampling Distribution of

  11. Estimatingp1-p2 • For large samples, point estimates and their margin of error as well as confidence intervals are based on the standard normal (z) distribution.

  12. Example • Compare the proportion of male and female college students who said that they had played on a soccer team during their K-12 years using a 99% confidence interval.

  13. Example, continued • Could you conclude, based on this confidence interval, that there is a difference in the proportion of male and female college students who said that they had playedon a soccer team during their K-12 years? • The confidence interval does not contains the value p1-p2 = 0. Therefore, it is not likely that p1= p2. You would conclude that there is a difference in the proportions for males and females. A higher proportion of males than females played soccer in their youth.

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