5. [13 marks] In CityVille, suppose that it has been assumed that 40% of the residents believe that taxes are too high,

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5 13 Marks In Cityville Suppose That It Has Been Assumed That 40 Of The Residents Believe That Taxes Are Too High 1 (177.76 KiB) Viewed 38 times

5. [13 marks] In CityVille, suppose that it has been assumed that 40% of the residents believe that taxes are too high, based on the services that are offered to its citizens. A local politician is wondering if the residents' opinions have changed. In order to test this claim, a likelihood ratio test will be conducted. a. [3] Explain why a Binomial model is appropriate here. b. [3] Show that the likelihood ratio test statistic is given by: .) ő ( A(0) = 2n{ő log () + (1 – 7) log (1-6) }. c. [5] Suppose that a small poll was conducted and in a random sample of 180 residents, 81 agreed that taxes are too high, and thus, 99 disagreed. We want to conduct a likelihood ratio test in order to test: H : 0 = 0.4. Calculate the approximate p-value and use the guidelines from page 128 of the Course Notes to assess the amount of evidence against Ho, based on the data. Be sure to show all steps clearly and show all relevant work in your solution (as noted in question 1). d. [2] If we use an error level of 5%, would you reject or not reject Ho. You need to justify your answer for full credit. Hint: See page 129 of the Course Notes for some guidance. Note: This approach in hypothesis testing (i.e. reject / don't reject H, is being used less and less now, but does still get used.