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 2 added 28 characters in body edited Oct 13 '15 at 15:00 Tim♦ 66.3k1212 gold badges149149 silver badges248248 bronze badges How about the chi-square goodness-of-fit test. The null hypothesis is Ho: Blue Shoe Proportion = p = 0.3. Then the chi-square statistic is $$X2 = \sum{{(observed - expected)^2}\over{observed}}$$ = (40 - 60*0.3)^2/(60*0.3) + (20 - 60*0.7)^2/(60*0.7) = 38.41. If you compare this to the null distribution, which is chi-square with df = 1, you get a p-value around 6e-10: chisq.test(c(40,20),p=c(0.3,0.7)) > chisq.test(c(40,20),p=c(0.3,0.7)) Chi-squared test for given probabilities data: c(40, 20) X-squared = 38.4127, df = 1, p-value = 5.726e-10 data: c(40, 20) X-squared = 38.4127, df = 1, p-value = 5.726e-10 How about the chi-square goodness-of-fit test. The null hypothesis is Ho: Blue Shoe Proportion = p = 0.3. Then the chi-square statistic is $$X2 = \sum{{(observed - expected)^2}\over{observed}}$$ = (40 - 60*0.3)^2/(60*0.3) + (20 - 60*0.7)^2/(60*0.7) = 38.41. If you compare this to the null distribution, which is chi-square with df = 1, you get a p-value around 6e-10: chisq.test(c(40,20),p=c(0.3,0.7)) Chi-squared test for given probabilities data: c(40, 20) X-squared = 38.4127, df = 1, p-value = 5.726e-10 How about the chi-square goodness-of-fit test. The null hypothesis is Ho: Blue Shoe Proportion = p = 0.3. Then the chi-square statistic is $$X2 = \sum{{(observed - expected)^2}\over{observed}}$$ = (40 - 60*0.3)^2/(60*0.3) + (20 - 60*0.7)^2/(60*0.7) = 38.41. If you compare this to the null distribution, which is chi-square with df = 1, you get a p-value around 6e-10: > chisq.test(c(40,20),p=c(0.3,0.7)) Chi-squared test for given probabilities data: c(40, 20) X-squared = 38.4127, df = 1, p-value = 5.726e-10 1 answered Oct 13 '15 at 9:04 AlaskaRon 1,49466 silver badges88 bronze badges How about the chi-square goodness-of-fit test. The null hypothesis is Ho: Blue Shoe Proportion = p = 0.3. Then the chi-square statistic is $$X2 = \sum{{(observed - expected)^2}\over{observed}}$$ = (40 - 60*0.3)^2/(60*0.3) + (20 - 60*0.7)^2/(60*0.7) = 38.41. If you compare this to the null distribution, which is chi-square with df = 1, you get a p-value around 6e-10: chisq.test(c(40,20),p=c(0.3,0.7)) Chi-squared test for given probabilities data: c(40, 20) X-squared = 38.4127, df = 1, p-value = 5.726e-10