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STA2020F 2006 TEST 2 - STA2020F 2006 Class Test 2 Date 9...

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STA2020F 2006 Class Test 2 Date: 9 May 2006 Time: 1 hour 30 minutes Total marks: 60 Instructions: Answer all the questions in your blue answer book. A formula sheet and the relevant statistical tables are provided at the end of this test paper. Question 1. An article reports histamine levels in the saliva of two groups of people, those suffering from allergies and those without. The data below form part of this article. With allergies: 67.6 39.6 111.2 Without: 34.3 39.6 48.0 4.7 45.5 There is reason to doubt that these samples were drawn from normally distributed populations. Carry out a suitable test of hypothesis to decide if the two groups differ in location. Be sure to state null and alternative hypotheses, show how you calculate the test statistic and provide a clear conclusion to the test, including a P-value. [6] Question 2. Polygraphs (lie detectors) are increasingly being used in many different areas of work. These machines depend on measuring small changes in the skin potential as a subject is asked a series of questions. The data below come from a bigger study in which independent groups of people were measured when feeling emotions of fear, happiness, depression and calmness. Fear: 23.1 57.6 10.5 Happiness: 22.7 53.2 9.7 19.6 Depression: 22.5 53.7 31.0 Calmness: 14.8 13.3 Use a suitable nonparametric test to investigate possible differences in location between these four groups. [8] Question 3. A topic of major concern to demographers and economists alike is the effect of a high fertility rate on per capita income. Fertility rates are often approximated by examining the percentage of the population under the age of fifteen. An economist would like to develop a model to predict per capita income (in dollars) based on the percentage of the population under the age of fifteen. A random sample of developing countries in Latin America and Africa is selected and the per capita income and percentage of the
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population under the age of fifteen is recorded. The economist believes that the
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