4. (18 points) Let X be a discrete random variable that takes values in {0, 1, 2, 3). We observe 100 independent realiza

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4 18 Points Let X Be A Discrete Random Variable That Takes Values In 0 1 2 3 We Observe 100 Independent Realiza 1 (110.48 KiB) Viewed 22 times

4. (18 points) Let X be a discrete random variable that takes values in {0, 1, 2, 3). We observe 100 independent realizations of X. The results are given in Table 1. We wish to test the null X Count 0 13 1 38 2 37 3 12 Table 1: 100 independent observations of a discrete random variable. hypothesis that X has a binomial distribution with n = 3 and p = 0.5 (i.e. the parameters are specified, not estimated). (a) Perform a chi-square test of the null hypothesis. Include a test statistic, p-value, and conclusion. (b) How do you interpret this p-value? Do you have any opinion or comments about the data or test based on your p-value? (c) An alternative test statistic is sup F(x) - F₁(z) where F(x) is the distribution function of a Binomial (3, 0.5) random variable, and F(x) is the empirical distribution function. Calculate the value of this test statistic.