STATISTICS â UNDERSTANDING HYPOTHESIS TESTS

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Statistics – Understanding Hypothesis Tests:Proportions201428. The formula for the standard error of the estimate, se( pˆquestionˆ1- pquestion2),is:2(1 - pˆ) + (1 ˆ ) (ˆ ˆquestion1 - pquestion2- pquestion1- pquestion2)(1)254(2)(3)(4)(5)(ˆ p + pˆ) - (ˆ p+ pˆquestion1 question2question1question2254pˆ ˆ ˆ (1 ˆquestion1(1- pquestion1)pquestion2- pquestion2)+25425422pˆquestionpˆ-254 2541 question2(ˆ p + pˆ) - (ˆ p - pˆquestion1 question2question1question2254))22Questions 29 to 31 refer to the following information.During 1999, students enrolled in stage one statistics at the University ofAuckland were surveyed regarding their access to, and experience with,computers. The survey was included as a question in an assignment, andstudents were given marks for completing it (irrespective of the answers theygave). Staff administering the courses wished to use the results of this surveyto draw conclusions about future stage one statistics students.One question asked: ‘At the start of the course, how would you describe yourExcel experience?’. A total of 918 students answered this question. Each of the918 answers were classified according to the response given by the student,and the stream the student attended. The results are given in the table below,where 107, 108 and 101 refer to the various streams.StreamResponse 107 108 101 TotalNone 15 36 102 153Very Little 44 89 119 252Some 74 150 200 424Lots 9 29 51 89Total 142 304 472 91829. A statistical test is performed on the data for no difference between theproportion of 107 students who responded None and the proportion of101 students who responded None. Which one of the followingstatements about this test is true?(1) The degrees of freedom used depends on the number of 107 and101 students in the sample.(2) The Wilcoxon rank-sum test could be used.© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 32 of 44The University of Auckland
Statistics – Understanding Hypothesis Tests:Proportions2014(3) The test should be two–tailed.(4) The test could only be used to show a difference existed in thesample proportions.(5) An appropriate null hypothesis is that the difference between theproportion of 107 students who responded None and the proportionof 101 students who responded None, is not zero.30. The standard error for the difference in the proportions tested in question29 is:(1) 0.033(2) 0.022(3) 0.023(4) 0.032(5) 0.18431. The P-value for the statistical test mentioned in question 29 is 0.004.Which one of the following statements gives the best interpretation ofthis P–value?(1) There is some evidence that the underlying proportions of 107students and 101 students that would respond None are different.(2) There is strong evidence that the sample proportions of 107students and 101 students that responded None are different.(3) There is strong evidence that the underlying proportions of 107students and 101 students that would respond None are different.(4) There is no evidence that the underlying proportions of 107students and 101 students that would respond None are different.(5) There is weak evidence that the underlying proportions of 107students and 101 students that would respond None are different.32. Which one of the following statements is false?(1) In a t-test for no difference between two proportions, being able todemonstrate that the difference was of practical significance(importance) would almost always imply statistical significance.(2) In hypothesis testing, large samples can lead to small P-valueswithout the results having any practical significance (importance).(3) In hypothesis testing, statistical significance does not implypractical significance (importance).(4) In a hypothesis test for no difference between two proportions, avery small P-value always indicates a very large difference in theproportions.(5) In hypothesis testing, a nonsignificant test result does not implythat the null hypothesis is true.© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 33 of 44The University of Auckland
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STATISTICS â UNDERSTANDING HYPOTHESIS TESTS