Question

State the null hypothesis.

Sally was interested in whether the number of m&m's was uniform over all 6 colors (the same number of m&m's for each color). The table categorizes the number of m&m's of each color found in an 1-pound bag.

	Color
	Brown	Red	Yellow	Blue	Orange	Green
Number	70	85	81	79	93	96

State the appropriate null hypothesis for a Chi-square goodness-of-fit test.

Question 21 options:

	H0: μ=1/6
	H0: The proportion for at least one of the colors is not 1/6
H0:  The proportion of each color is 1/6
	H0: The number of m&m's is independent of color

Answer 1

Solution:

Given: Sally was interested in whether the number of m&m's was uniform over all 6 colors (the same number of m&m's for each color).

We have to state the appropriate null hypothesis for a Chi-square goodness-of-fit test.

Under null hypothesis for a Chi-square goodness-of-fit test, we assume all categories are equally distributed or distributed according to specific distribution or distributed according to expected proportions.

Since we are expecting the number of m&m's was uniform over all 6 colors, that is the proportion of each of 6 color is 1/6.

thus correct answer is:

H0:  The proportion of each color is 1/6

Option 1 is incorrect , since it states about mean = 1/6 instead of proportions.

Option 2 is incorrect, since Under null hypothesis for a Chi-square goodness-of-fit test, we assume all categories are equally distributed, not the different.

Option 4 is incorrect , since independence is assumed in Chi-square independence of attributes, not in Chi-square goodness-of-fit test.