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Question 3 On June 28, 2012 the U.S. Supreme Court upheld the much debated 2010 healthcare law, declaring it constitutional. A Gallup poll released the day after this decision indicates that 46% of 1,012 Americans agree with this decision. At a 95% confidence level, this sample has a 3% margin of error. (b) How would you formulate a hypothesis test for the following claim "Majority of Americans think the 2010 healthcare law is unconstitutional"? What is your null hypothesis? What is your alternative hypothesis? (Here "majority" means "more than 50%".) (c) What is the sampling distribution for X = nô under your null hypothesis? (d) Calculate p-value for the test problem in part (b) using the data based on the Gallup poll, based on the sampling distribution in part (c). (e) How can you approximate the distribution of X under the null hypothesis using normal approximation to Binomial distribution? Draw the normal density curve and shade the area corresponding to your p-value calculation (Hint: use pnorm or normTail). (f) Based on the p-value in part (d), what conclusion can you draw at significance level 0.01?

Question 3 On June 28, 2012 the U.S. Supreme Court upheld the much debated 2010 healthcare law, declaring it constitutional. A Gallup poll released the day after this decision indicates that 46% of 1,012 Americans agree with this decision. At a 95% confidence level, this sample has a 3% margin of error. (b) How would you formulate a hypothesis test for the following claim "Majority of Americans think the 2010 healthcare law is unconstitutional"? What is your null hypothesis? What is your alternative hypothesis? (Here "majority" means "more than 50%".) (c) What is the sampling distribution for X = nô under your null hypothesis? (d) Calculate p-value for the test problem in part (b) using the data based on the Gallup poll, based on the sampling distribution in part (c). (e) How can you approximate the distribution of X under the null hypothesis using normal approximation to Binomial distribution? Draw the normal density curve and shade the area corresponding to your p-value calculation (Hint: use pnorm or normTail). (f) Based on the p-value in part (d), what conclusion can you draw at significance level 0.01?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 6E: List the sample space of each experiment. Tossing three coins
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Question 3 On June 28, 2012 the U.S. Supreme Court upheld the much debated 2010 healthcare law, declaring it constitutional. A Gallup poll released the day after this decision indicates that 46% of 1,012 Americans agree with this decision. At a 95% confidence level, this sample has a 3% margin of error. (b) How would you formulate a hypothesis test for the following claim "Majority of Americans think the 2010 healthcare law is unconstitutional"? What is your null hypothesis? What is your alternative hypothesis? (Here "majority" means "more than 50%".) (c) What is the sampling distribution for X = nô under your null hypothesis? (d) Calculate p-value for the test problem in part (b) using the data based on the Gallup poll, based on the sampling distribution in part (c). (e) How can you approximate the distribution of X under the null hypothesis using normal approximation to Binomial distribution? Draw the normal density curve and shade the area corresponding to your p-value calculation (Hint: use pnorm or normTail). (f) Based on the p-value in part (d), what conclusion can you draw at significance level 0.01?
Transcribed Image Text:Question 3 On June 28, 2012 the U.S. Supreme Court upheld the much debated 2010 healthcare law, declaring it constitutional. A Gallup poll released the day after this decision indicates that 46% of 1,012 Americans agree with this decision. At a 95% confidence level, this sample has a 3% margin of error. (b) How would you formulate a hypothesis test for the following claim "Majority of Americans think the 2010 healthcare law is unconstitutional"? What is your null hypothesis? What is your alternative hypothesis? (Here "majority" means "more than 50%".) (c) What is the sampling distribution for X = nô under your null hypothesis? (d) Calculate p-value for the test problem in part (b) using the data based on the Gallup poll, based on the sampling distribution in part (c). (e) How can you approximate the distribution of X under the null hypothesis using normal approximation to Binomial distribution? Draw the normal density curve and shade the area corresponding to your p-value calculation (Hint: use pnorm or normTail). (f) Based on the p-value in part (d), what conclusion can you draw at significance level 0.01?
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