STATISTICS â UNDERSTANDING HYPOTHESIS TESTS

More documents

Recommendations

Info

$LaTeX for Document Preparation - The University of Auckland Library$

Statistics – Understanding Hypothesis Tests:Proportions2014Questions 24 to 28 refer to the following information.The Washington Post, The Henry J Kaiser Family Foundation and HarvardUniversity conducted a poll (8 March – 22 April, 2001) ‘to gauge the racialattitudes of American adults’. The telephone poll surveyed 1709 adultsincluding 779 whites, 323 African Americans, 315 Hispanics and 254 AsianAmericans. Assume this sample of 1709 adults is a random sample ofAmerican adults. Two of the questions in the survey were:Question 1:Do you feel that African Americans have more, less or about the sameopportunities in life as whites have?andQuestion 2:Do you feel that Asian Americans have more, less or about the sameopportunities in life as whites have?The percentage results for these two questions are shown in Table 7 below.ResponseSampleMore % Less % Same % Unsure % sizeQuestion 1White 13 27 58 2 779African American 1 74 23 2 323Hispanic 8 46 44 2 315Asian American 10 44 39 7 254Total Sample 11 35 51 2 1709Question 2White 13 14 70 4 779African American 15 38 39 8 323Hispanic 18 24 55 3 315Asian American 7 34 53 5 254Total Sample 14 18 63 4 1709Table 7: Americans’ responses to racial attitudes surveyLet p more be the proportion of whites who feel that African Americans havemore opportunities in life than whites have and p less be the proportion ofwhites who feel that African Americans have less opportunities in life thanwhites have. (Ie, whites’ responses to Question 1.)24. An estimate of the difference between p more and p less is:(1) 0.018(4) 0.01(2) -0.01(5) -0.10(3) -0.14© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 30 of 44The University of Auckland
Statistics – Understanding Hypothesis Tests:Proportions201425. Information from Table 7 above, is used to construct a 95% confidenceinterval for the difference p more - p less . For the purpose of calculatingse( pˆmore- pˆless), the sampling situation can be described as:(1) two independent samples of sizes 779 and 254.(2) one sample of size 779, several response categories.(3) one sample of size 1709, many yes/no items.(4) one sample of size 1709, several response categories.(5) one sample of size 779, many yes/no items.26. A 95% confidence interval for the difference p more - p less is(-0.1833, -0.09668). The best interpretation of this interval is:With 95% confidence, the percentage of whites who feel that AfricanAmericans have more opportunities in life than whites have issomewhere between:(1) 10% higher than and 18% lower than the percentage who feel thatAfrican Americans have less opportunities in life than whites have.(2) 10% and 18%.(3) 10% and 18% higher than the percentage who feel that AfricanAmericans have less opportunities in life than whites have.(4) 10% lower than and 18% higher than the percentage who feel thatAfrican Americans have less opportunities in life than whites have.(5) 10% and 18% lower than the percentage who feel that AfricanAmericans have less opportunities in life than whites have.Questions 27 and 28 refer to the following additional information.Let:p question1 be the proportion of Asian Americans who feel that AfricanAmericans have more opportunities in life than whites haveandp question2 be the proportion of Asian Americans who feel that AsianAmericans have more opportunities in life than whites have.Information from Table 7, is used to conduct a 2-tailed test for no differencebetween p question1 and p question2 .27. The expression for evaluating the test statistic for the null hypothesis,H 0 : p question1 - p question2 = 0, is:(1)se(ˆppˆ- pˆquestion1question1question2) + se(ˆpquestion2)(4)pˆse(ˆpquestion1question1- pˆquestion2- pˆquestion2)(2)se(ˆppˆquestion1question1)2- pˆquestion2- se(ˆpquestion2)2(5)sep- pquestion1question2( pˆˆquestion1- pquestion2)(3)se pˆp - pquestion1question2(question1question2) + se(ˆp)© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 31 of 44The University of Auckland
Page 1: Statistics - Understanding Hypothes
Page 5 and 6: Statistics - Understanding Hypothes
Page 11 and 12: Step 1Statistics - Understanding Hy
Page 15 and 16: 1.Step 7Statistics - Understanding
Page 17 and 18: Step 9Statistics - Understanding Hy
Page 29: Statistics - Understanding Hypothes

STATISTICS â UNDERSTANDING HYPOTHESIS TESTS

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?

STATISTICS â UNDERSTANDING HYPOTHESIS TESTS