Question

In RuPaul's Drag Race, drag queens are often categorized as in one of four categories (Pageant Queens, Comedy Queens, Look Queens, or Dancing Queens). Shangela want to test the hypothesis that the proportion of All drag queens who are Pageant Queens is 2, the proportion that are Comedy Queens is 25, the proportion that are Look Queens is .15, and the proportion that are Dancing Queens is .4 Shangela collects a sample of 56 drag queens. In her sample of 56 queens, 20 are Pageant Queens, 15 are Comedy Queens, 10 are Look Queens, and 11 are Dancing Queens. Let's say that Shangela finds the chi-squared statistic to be 9.57. Find the correct p-value to 2 decimal places. Answer:

Answer 1

Here,

Under H₀, the test statistic follows a chi square distribution with df = 4 - 1 = 3

P-value = $P(\chi^2_{3}>\chi^2_{obs}) = P(\chi^2_{3}>9.57) = 1 - 0.977402 = 0.0225980$