Conducting a Chi-Square Test for Goodness of Fit — Quiz
Question 5 • Statistics
A company is started by four friends. The company was Erica’s idea, so she wants to fill 70 percent of the orders. Jen, Heather, and Tonya each agree to fill 10 percent of the orders. After a successful first year, Erica wants to determine if the distribution of the number of orders filled is adhering to the agreed-upon percentages. To do so, she selects a random sample of 100 orders from the large number of orders that were filled and determines who filled the order. What are the appropriate hypotheses for this test?
Answer
A
cap h sub 0 : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1 cap h sub A : Not all of the p sub i 's are as stated.
B
cap h sub 0 : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1 cap h sub A : p sub Erica is not equal to 0 point 7 , p sub Jen is not equal to 0 point 1 , p sub Heather is not equal to 0 point 1 , p sub Tonya is not equal to 0 point 1
C
cap h sub 0 : p sub Erica is not equal to 0 point 7 , p sub Jen is not equal to 0 point 1 , p sub Heather is not equal to 0 point 1 , p sub Tonya is not equal to 0 point 1 cap h sub A : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1
D
cap h sub 0 : Not all of the p sub i 's are as stated. cap h sub A : p sub Erica is equal to 0 point 7 , p sub Jen is equal to 0 point 1 , p sub Heather is equal to 0 point 1 , p sub Tonya is equal to 0 point 1
Explanation
This is a chi-square goodness-of-fit test comparing the observed order shares with the agreed percentages. The null hypothesis states that all four population proportions match the agreement: Erica 0.70, and Jen, Heather, and Tonya each 0.10. The alternative is that at least one proportion differs, which is expressed by “not all” of the proportions being as stated. Thus, choice A is correct; the alternative does not require every proportion to differ.
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