STATISTICS – UNDERSTANDING HYPOTHESIS TESTS

Statistics – Understanding Hypothesis Tests:Proportions2014Question 7 refers to the following information.Results from two independent polls of voting intentions, taken in July andAugust 1993, were reported in TIME (20 September, 1993). There were 950voters sampled in each poll. The results were:Preferred Party (%)Alliance Labour National NZ FirstJuly 18 36 38 -August 12.5 38 36.5 11.5There was some interest in whether the NZ First party had a bigger impact onthe Labour or the National vote. To investigate this, a test was conducted ofthe null hypothesis that there was no change in p L – p N , the Labour-Nationaldifference, between the two polls. The resulting P-value was 0.76.7. Which of the following statements is true?(1) There is no evidence at the 5% level that NZ First has had animpact on support for either Labour or National.(2) The probability that NZ First has had no impact on the differencebetween National and Labour is 0.76.(3) A 95% confidence interval for the difference between National andLabour would not contain zero.(4) There is no evidence at the 5% significance level that thedifference between National and Labour has changed.(5) The probability that NZ First has had an impact on the differencebetween National and Labour is 0.76.8. Which one of the following statements is false?(1) In hypothesis testing, statistical significance does not implypractical significance.(2) In a hypothesis test for no difference between two proportions, avery small P-value indicates a very large difference in theproportions.(3) In hypothesis testing, a non-significant test result does not implythat H 0 is true.(4) In hypothesis testing, large samples can lead to small P-valueswithout the results having any practical significance.(5) In a hypothesis test for no difference between two proportions, atwo-sided test should be used when the idea of doing the test hasbeen triggered as a result of looking at the data.© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 23 of 44The University of Auckland