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  • Slide 1
  • Population Sample Parameter: Proportion p Count Mean Median Statistic: Proportion Count Mean Median
  • Slide 2
  • Estimate population proportion, with a confidence interval, from data of a random sample.
  • Slide 3
  • Population Proportion = p Sample p
  • Slide 4
  • Population Proportion = p Sample p There is 95% chance that will fall inside the interval ND
  • Slide 5
  • Population Sample Proportion = p p There is 95% chance that will fall inside the interval
  • Slide 6
  • Population Sample Proportion = p p There is 95% chance that will fall inside the interval
  • Slide 7
  • Open the Fathom file estimate1.ftm
  • Slide 8
  • The proportion of yes in the population is given by the slider value p. (In this example, p =0.75)
  • Slide 9
  • Assume that the population proportion is an unknown, and we are going to estimate it by suggesting a 95% confidence interval based on the data of one random sample. Size of this sample is n = 20.
  • Slide 10
  • The proportion of yes in this sample is The estimated standard deviation of is Margin of error = 2(0.080) = 0.160 The 95% confidence interval is (0.85 0.16, 0.85 + 0.16) or (0.69, 1.01)
  • Slide 11
  • Based on the result of this sample, we are 95% confident that the true proportion p lies between 0.69 and 1.01. Note that the interval will vary from sample to sample, but if we repeat the sampling process indefinitely with samples of the same size, we will expect 95% of these intervals to capture the true proportion. To shorten the interval, we have to increase the sample size. 00.20.40.60.81 95% conf. Int.
  • Slide 12
  • Note that the interval will vary from sample to sample, but if we repeat the sampling process indefinitely with samples of the same size, we will expect 95% of these intervals to capture the true proportion. 00.20.40.60.81 Confidence Intervals from different samples
  • Slide 13
  • Use an experiment record sheet to record more confidence intervals from other samples of the same size.
  • Slide 14
  • Some intervals may not be able to capture the true proportion.
  • Slide 15
  • To estimate with a larger sample, double click on the Sample of Data collection to open its inspector and adjust the sample size.
  • Slide 16
  • The proportion of yes in this sample is and the sample size is n = 80. The estimated standard deviation of is Margin of error = 2(0.0467) = 0.0934 The 95% confidence interval is (0.775 0.0934, 0.775 + 0.0934) or (0.682, 0.868)
  • Slide 17
  • 00.20.40.60.81 95% conf. Int. Sample size = 20 00.20.40.60.81 95% conf. Int. Sample size = 80 We are now 95% confident that the true proportion lies between 0.682 and 0.868. The interval is shorter when the sample size is increased from 20 to 80.
  • Slide 18
  • Example: Halloween Practices and Beliefs An organization conducted a poll about Halloween practices and beliefs in 1999. A sample of 1005 adult Americans were asked whether someone in their family would give out Halloween treats from the door of their home, and 69% answered yes. Construct a 95% confidence interval for p, the proportion of all adult Americans who planned to give out Halloween treats from their home in 1999. Adapted from Rossman et al. (2001, p.433)
  • Slide 19
  • Sample size = 1005 Sample proportion = 0.69 Estimated standard deviation of sample proportions = Margin of error = 2(0.0146) = 0.0292 95% confidence interval is 0.69 0.0292 We are 95% confident that the population proportion lies between 0.6608 and 0.7192. 00.20.40.60.81 95% conf. Int.
  • Slide 20
  • Example: Personal Goal According to a survey in a university, 132 out of 200 first-year students in a random sample have identified being well-off financially as an important personal goal. Give a 95% confidence interval for the proportion of all first- year students at the university who would identify being well- off as an important personal goal. Adapted from Moore & Mccabe (1999, p.597)
  • Slide 21
  • Sample size = 200 Sample proportion = 132/200 = 0.66 Estimated standard deviation of sample proportions = Margin of error = 2(0.0335) = 0.067 95% confidence interval is 0.66 0.067 We are 95% confident that the population proportion lies between 0.593 and 0.727. 00.20.40.60.81 95% conf. Int.
  • Slide 22
  • Estimate population mean, with a confidence interval, from data of a random sample.
  • Slide 23
  • Population Mean = Sample
  • Slide 24
  • Population Mean = Sample s.d. = There is 95% chance that will fall inside the interval ND
  • Slide 25
  • Population Sample Mean = s.d. = There is 95% chance that will fall inside the interval
  • Slide 26
  • Population Sample Mean = s.d. = s There is 95% chance that will fall inside the interval
  • Slide 27
  • Open the Fathom file estimate2.ftm
  • Slide 28
  • This summary table record the true mean and standard deviation of the population, where are supposed to be unknowns.
  • Slide 29
  • Assume that the population mean is an unknown, and we are going to estimate it by suggesting a 95% confidence interval based on the data of one random sample. Size of this sample is n = 20.
  • Slide 30
  • The sample mean and standard deviation are The estimated standard deviation of is Margin of error = 2(4.52) = 9.046 The 95% confidence interval is (29.85 9.05, 29.85 + 9.05) or (20.80, 38.90)
  • Slide 31
  • Based on the result of this sample, we are 95% confident that the true mean lies between 20.80 and 38.90. Note that the interval will vary from sample to sample, but if we repeat the sampling process indefinitely with samples of the same size, we will expect 95% of these intervals to capture the true mean. To shorten the interval, we have to increase the sample size. 01020304050 95% conf. Int.
  • Slide 32
  • Example: Protein Intake A nutritional study produced data on protein intake for women. In a sample of n = 264 women, the mean of protein intake is grams and the standard deviation is s = 30.5 grams. Estimate the population mean and give a 95% confidence interval. Adapted from Bennett et al. (2001, p.401)
  • Slide 33
  • Estimated standard deviation of the sample means = Margin of Error = 2(1.9) = 3.8 grams 95% confidence interval is 59.6 3.8 grams We can say with 95% confidence that the interval ranging from 55.8 grams to 63.4 grams contains the population mean.
  • Slide 34
  • Example: Body Temperature A study by University of Maryland researchers investigated the body temperatures of n = 106 subjects. The sample mean of the data set is and the standard deviation for the sample is. Estimate the population mean body temperature with a 95% confidence interval. Adapted from Bennett et al. (2001, p.403)
  • Slide 35
  • Estimated standard deviation of the sample means = Margin of Error = 2(0.06 F) = 0.12 F 95% confidence interval is 98.20 F 0.12 F We can say with 95% confidence that the interval ranging from 98.08 F to 98.32 F contains the population mean.
  • Slide 36
  • Normal Distribution m smm 2sm 3sm + sm + 2sm + 3s 68% 95% 99.7%

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