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sample2 - Sample Problems Statstics 517 1 In a contingency...

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Sample Problems Statstics 517 1. In a contingency table, 1000 individuals are classified by gender and by whether they favor, oppose, or have no opinion on a complete ban on smoking in public places. The data is the following. Smoking in Public Places Favor Oppose No Opinion Totals Male 258 228 10 496 Female 297 202 5 504 Totals 555 430 15 1000 (a) Test the null hypothesis that gender and opinion on smoking in public places are independent at α = 0 . 1. Interpret the result in plain English. (b) What is the approximate p -value of the above test? Chi-square percentiles, χ 2 df,α χ 2 2 , 0 . 1 χ 2 2 , 0 . 05 χ 2 2 , 0 . 01 χ 2 6 , 0 . 1 χ 2 6 , 0 . 05 χ 2 6 , 0 . 01 4.60517 5.991465 9.21034 10.64464 12.59159 16.81189 2. Let X 1 , · · · , X n be a random sample from a geometric distribution with paramater θ , i.e., f ( x ; θ ) = θ (1 - θ ) x , x = 0 , 1 , 2 , · · · , 0 < θ < 1 You may consider X as the number of failures before we see the first success in a series of independent Bernoulli experiments. The success probability for each trial is θ .
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