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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
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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