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Homework3 - be a 2 × 2 table of expected counts(b State...

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STA 3024: Homework 3 (Extra credit: 10 points) (Due Monday July 19) Suppose we want to investigate the gateway drug theory—the idea that marijuana use can lead to use of more serious drugs, such as cocaine and heroin. We distribute an anonymous questionnaire to a random sample of 166 UF students that asks whether they have ever used marijuana and whether they have ever used cocaine or heroin. Our results are summarized by the following contingency table: Cocaine/Heroin Marijuana Yes No Total Yes 8 54 62 No 10 94 104 Total 18 148 166 1. For our sample data, calculate the conditional distribution of whether or not students have used cocaine/heroin, given whether or not they have used marijuana. (Your answer should be a 2 × 2 table of conditional percentages.) 2. Now let’s use this data to conduct a chi-squared test with α = 0 . 05. (a) Calculate each cell’s expected count for the chi-squared test. (Your answer should
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Unformatted text preview: be a 2 × 2 table of expected counts.) (b) State the assumptions made by the chi-squared test. For each assumption, state whether or not it is satisfied by our data. (c) State the hypotheses for the chi-squared test. (d) Calculate the value of the Chi-square test statistic, χ 2 . (e) In the following step, we will compare this observed χ 2 value to a chi-squared distri-bution. What df should this chi-squared distribution have? (f) Find the p-value as best you can (i.e., “between 0.025 and 0.05”) using a chi-squared table or any other method of your choice. (g) Use this p-value to make a decision, and interpret this decision in the context of the actual variables. (Your interpretation should be understandable by someone who doesn’t know anything about this data or about statistics in general.)...
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