# Section 6.1-D Distribution of a Proportion Statistics: Unlocking

Section 6.1-D Distribution of a Proportion Statistics: Unlocking the Power of Data Lock5 Review The Central Limit Theorem applies to the distribution of the a) statistic b) parameter c) null value d) data e) standard error Statistics: Unlocking the Power of Data

Lock5 Owned Homes The 2010 census reports that, of all the nations occupied housing units, 65.1% are owned by the occupants. The SE is 0.048. If we were to take random samples of 100 homes, what would be the distribution of ? a) N(0.651, 0.048) b) N(0.048, 0.651) c) N(0, 0.048) d) N(0, 0.651) Statistics: Unlocking the Power of Data Lock5

Bi-Lingual in Oregon The 2010 census reports that 14.6% of the residents of Oregon speak a language other than English at home. If we were to take random samples of 100 residents, what would the standard error of be? a) 0.146 b) 0.0146 c) 0.035 d) 0.0035 Statistics: Unlocking the Power of Data Lock5 Bi-Lingual in Oregon The 2010 census reports that 14.6% of the

residents of Oregon speak a language other than English at home. Recall that SE = 0.035. If we were to take random samples of 100 residents, what would be the distribution of ? a) N(0,0.146) b) N(0,0.035) c) N(0.035,0.146) d) N(0.146,0.035) Statistics: Unlocking the Power of Data Lock5 Section 6.1-CI Confidence Interval for a Proportion

Statistics: Unlocking the Power of Data Lock5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the sample proportion? A. B. C. D. E. 280 500 56

0.56 1.96 Statistics: Unlocking the Power of Data Lock5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the value of z*? A. B. C. D. E. 0.56

1.28 1.645 1.96 2.576 Statistics: Unlocking the Power of Data Lock5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the standard error? A. B. C. D. E.

0.56 500 0.00049 0.0365 0.0222 =0.0222 Statistics: Unlocking the Power of Data Lock5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the margin of error? A.

B. C. D. E. 0.56 500 0.00049 0.0365 0.0222 CI = statistic margin of error Statistics: Unlocking the Power of Data Lock5 Margin of Error CI: *

For a single proportion, what is the margin of error? a) b) * c) 2 * CI = statistic margin of error Statistics: Unlocking the Power of Data Lock5 Margin of Error n Suppose we want to estimate a proportion with a margin of error of 0.03 with 95% confidence. How large a sample size do we need? (a) (b)

(c) (d) About 100 About 500 About 1000 About 5000 Statistics: Unlocking the Power of Data n Lock5 Section 6.1-HT Hypothesis Test for a Proportion

Statistics: Unlocking the Power of Data Lock5 Baseball Home Field Advantage 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. Statistics: Unlocking the Power of Data Lock5 Baseball Home Field Advantage Counts are greater than 10 in each category H0 : p = 0.5 Ha : p > 0.5 = ^ 0 0 (1 0 )

= 0.549 0.5 0.049 = =4.86 0.01 0.5(1 0.5) 2430 p-value = 6.2 10-7 Based on this data, there is strong evidence of a home field advantage in major league baseball. Lock5

Statistics: Unlocking the Power of Data 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. B. C. D. Right-tailed Left-tailed Two-tailed No-tailed Statistics: Unlocking the Power of Data

Lock5 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. E. 0.0222 0.0365 0.02236 0.04 0.06329

Statistics: Unlocking the Power of Data We use the null proportion 0.5 in computing the standard error for the test. Lock5 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. 2.703 25.225 25.045 2.683 0.05 =2.683 Statistics: Unlocking the Power of Data Lock5 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=2.683. What is the p-value? A. B. C. D. E. 0.0072 0.0036 0.036 0.072 0.05 Statistics: Unlocking the Power of Data Lock5

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 H0 and conclude that more than half of US citizens plan to vote. B. Reject H0 and conclude that it is not true that more than half of US citizens plan to vote. C. Do not reject H0 and conclude that more than half of US citizens plan to vote. D. Do not reject H0 and conclude that it is not true that more than half of US citizens plan to vote. Statistics: Unlocking the Power of Data Lock5

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