Statistics: Unlocking the Power of Data Lock 5 Section 6.3 Test for a Single Proportion.

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Presentation transcript:

Statistics: Unlocking the Power of Data Lock 5 Section 6.3 Test for a Single Proportion

Statistics: Unlocking the Power of Data Lock 5 Outline Test for a single proportion

Statistics: Unlocking the Power of Data Lock 5 Hypothesis Testing For hypothesis testing, we want the distribution of the sample proportion assuming the null hypothesis is true What to use for p?

Statistics: Unlocking the Power of Data Lock 5 Test for a Single Proportion If np 0 ≥ 10 and n(1 – p 0 ) ≥ 10, then the p-value can be computed as the area in the tail(s) of a standard normal beyond z.

Statistics: Unlocking the Power of Data Lock 5 Of the 2430 Major League Baseball (MLB) games played in 2009, the home team won in 54.9% of the games. If we consider 2009 as a representative sample of all MLB games, is this evidence of a home field advantage in Major League Baseball? (a) Yes (b) No (c) No idea The p-value is very small, so we have very strong evidence of a home field advantage. Baseball Home Field Advantage

Statistics: Unlocking the Power of Data Lock 5 Baseball Home Field Advantage Counts are greater than 10 in each category Based on this data, there is strong evidence of a home field advantage in major league baseball. H 0 : p = 0.5 H a : p > 0.5 p-value = 6.2  10 -7

Statistics: Unlocking the Power of Data Lock 5 Baseball Home Field Advantage

Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We want to test to see if this provides evidence that the proportion of US citizens who plan to vote is greater than half. Is this test: A.Right-tailed B.Left-tailed C.Two-tailed D.No-tailed

Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We want to test to see if this provides evidence that the proportion of US citizens who plan to vote is greater than half. What is the standard error for the test? A B C D.0.04 E We use the null proportion 0.5 in computing the standard error for the test.

Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We want to test to see if this provides evidence that the proportion of US citizens who plan to vote is greater than half. What is the test statistic? A B C D E.0.05

Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We want to test to see if this provides evidence that the proportion of US citizens who plan to vote is greater than half. The test statistic is z= What is the p-value? A B C D E.0.05

Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We want to test to see if this provides evidence that the proportion of US citizens who plan to vote is greater than half. What is the conclusion at a 5% level? A.Reject H 0 and conclude that more than half of US citizens plan to vote. B.Reject H 0 and conclude that it is not true that more than half of US citizens plan to vote. C.Do not reject H 0 and conclude that more than half of US citizens plan to vote. D.Do not reject H 0 and conclude that it is not true that more than half of US citizens plan to vote.