Is it unusual to observe a sample of 66 men with a sample proportion ( ) of 30% if the true population proportion (p) is 15%

Is it unusual to observe a sample of 66 men with a sample proportion ( ) of 30% if the true population proportion (p) is 15% www.phwiki.com

Is it unusual to observe a sample of 66 men with a sample proportion ( ) of 30% if the true population proportion (p) is 15%

Faller, Mary Beth, Health Reporter has reference to this Academic Journal, PHwiki organized this Journal If we live with a deep sense of gratitude, our life will be greatly embellished. Chapter 19 Inference about a Population Proportion BPS – 5th Ed. Chapter 19 Proportions BPS – 5th Ed. Chapter 19 The proportion of a population that has some outcome (“success”) is p. The proportion of successes in a sample is measured by the sample proportion:

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Inference about a Proportion Simple Conditions BPS – 5th Ed. Chapter 19 Inference about a Proportion Sampling Distribution BPS – 5th Ed. Chapter 19 Case Study BPS – 5th Ed. Chapter 19 Science News, Jan. 27, 1995, p. 451. Comparing Fingerprint Patterns

Case Study: Fingerprints BPS – 5th Ed. Chapter 19 Fingerprints are a “sexually dimorphic trait which means they are among traits that may be influenced by prenatal hormones.” It is known Most people have more ridges in the fingerprints of the right h in addition to . (People with more ridges in the left h in addition to have “leftward asymmetry.”) Women are more likely than men to have leftward asymmetry. Compare fingerprint patterns of heterosexual in addition to homosexual men. Case Study: Fingerprints Study Results BPS – 5th Ed. Chapter 19 66 homosexual men were studied. 20 (30%) of the homosexual men showed leftward asymmetry. 186 heterosexual men were also studied. 26 (14%) of the heterosexual men showed leftward asymmetry. Case Study: Fingerprints A Question BPS – 5th Ed. Chapter 19 Assume that the proportion of all men who have leftward asymmetry is 15%. Is it unusual to observe a sample of 66 men with a sample proportion ( ) of 30% if the true population proportion (p) is 15%

Case Study: Fingerprints Sampling Distribution BPS – 5th Ed. Chapter 19 Case Study: Fingerprints Answer to Question BPS – 5th Ed. Chapter 19 Where should about 95% of the sample proportions lie mean plus or minus two st in addition to ard deviations 0.15 2(0.044) = 0.062 0.15 + 2(0.044) = 0.238 95% should fall between 0.062 & 0.238 It would be unusual to see 30% with leftward asymmetry (30% is not between 6.2% & 23.8%). St in addition to ardized Sample Proportion BPS – 5th Ed. Chapter 19 Inference about a population proportion p is based on the z statistic that results from st in addition to ardizing : z has approximately the st in addition to ard normal distribution as long as the sample is not too small in addition to the sample is not a large part of the entire population.

Building a Confidence Interval Population Proportion BPS – 5th Ed. Chapter 19 St in addition to ard Error BPS – 5th Ed. Chapter 19 Since the population proportion p is unknown, the st in addition to ard deviation of the sample proportion will need to be estimated by substituting as long as p. Confidence Interval BPS – 5th Ed. Chapter 19

Case Study: Soft Drinks BPS – 5th Ed. Chapter 19 A certain soft drink bottler wants to estimate the proportion of its customers that drink another br in addition to of soft drink on a regular basis. A r in addition to om sample of 100 customers yielded 18 who did in fact drink another br in addition to of soft drink on a regular basis. Compute a 95% confidence interval (z = 1.960) to estimate the proportion of interest. Case Study: Soft Drinks BPS – 5th Ed. Chapter 19 We are 95% confident that between 10.5% in addition to 25.5% of the soft drink bottler’s customers drink another br in addition to of soft drink on a regular basis. The Hypotheses as long as Proportions BPS – 5th Ed. Chapter 19 Null: H0: p = p0 One sided alternatives Ha: p > p0 Ha: p < p0 Two sided alternative Ha: p ¹ p0 Test Statistic as long as Proportions BPS - 5th Ed. Chapter 19 Start with the z statistic that results from st in addition to ardizing : Assuming that the null hypothesis is true (H0: p = p0), we use p0 in the place of p: P-value as long as Testing Proportions BPS - 5th Ed. Chapter 19 Ha: p > p0 P-value is the probability of getting a value as large or larger than the observed test statistic (z) value. Ha: p < p0 P-value is the probability of getting a value as small or smaller than the observed test statistic (z) value. Ha: p p0 P-value is two times the probability of getting a value as large or larger than the absolute value of the observed test statistic (z) value. BPS - 5th Ed. Chapter 19 Case Study BPS - 5th Ed. Chapter 19 Brown, C. S., (1994) “To spank or not to spank.” USA Weekend, April 22-24, pp. 4-7. Parental Discipline What are parents’ attitudes in addition to practices on discipline Case Study: Discipline BPS - 5th Ed. Chapter 19 Nationwide r in addition to om telephone survey of 1,250 adults that covered many topics 474 respondents had children under 18 living at home results on parental discipline are based on the smaller sample reported margin of error 5% as long as this smaller sample Scenario Case Study: Discipline BPS - 5th Ed. Chapter 19 “The 1994 survey marks the first time a majority of parents reported not having physically disciplined their children in the previous year. Figures over the past six years show a steady decline in physical punishment, from a peak of 64 percent in 1988.” The 1994 sample proportion who did not spank or hit was 51% ! Is this evidence that a majority of the population did not spank or hit (Per as long as m a test of significance.) Reported Results Faller, Mary Beth Arizona Republic Health Reporter www.phwiki.com

Case Study: Discipline BPS – 5th Ed. Chapter 19 Null: The proportion of parents who physically disciplined their children in 1993 is the same as the proportion [p] of parents who did not physically discipline their children. [H0: p = 0.50] Alt: A majority (more than 50%) of parents did not physically discipline their children in 1993. [Ha: p > 0.50] The Hypotheses Case Study: Discipline BPS – 5th Ed. Chapter 19 Based on the sample n = 474 (large, so proportions follow Normal distribution) no physical discipline: 51% st in addition to ard error of p-hat: (where .50 is p0 from the null hypothesis) st in addition to ardized score (test statistic) z = (0.51 – 0.50) / 0.023 = 0.43 Test Statistic Case Study: Discipline BPS – 5th Ed. Chapter 19 P-value = 0.3336 From Table A, z = 0.43 is the 66.64th percentile. P-value

Case Study: Discipline BPS – 5th Ed. Chapter 19 Chapter 20 Comparing Two Proportions BPS – 5th Ed. Chapter 20 Two-Sample Problems BPS – 5th Ed. Chapter 20 The goal of inference is to compare the responses to two treatments or to compare the characteristics of two populations. We have a separate sample from each treatment or each population. The units are not matched, in addition to the samples can be of differing sizes.

Chapter 21 Inference about Variables: Part III Review BPS – 5th Ed. Chapter 21

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