A company is started by 4 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. She finds that Erica filled 56 orders, Jen filled 18 , Heather filled 14 , and Tonya filled 12 What is the value of the chi-square test statistic and the cap p -value of this test? Use the chi-square distribution table.
Answer
A
chi squared is equal to 11 point 2 0 , cap p -value is between 0 point 0 1 and 0 point 0 2
B
chi squared is equal to 8 point 5 3 , cap p -value is between 0 point 0 2 5 and 0 point 0 5
C
chi squared is equal to 8 point 5 3 , cap p -value is between 0 point 0 5 and 0 point 1 0
D
chi squared is equal to 11 point 2 0 , cap p -value is between 0 point 0 2 5 and 0 point 0 5
Explanation
The expected counts are 70 for Erica and 10 each for Jen, Heather, and Tonya. Using χ² = Σ(observed − expected)² / expected gives 2.8 + 6.4 + 1.6 + 0.4 = 11.2. There are 4 categories, so the degrees of freedom are 4 − 1 = 3. For 3 degrees of freedom, a chi-square value of 11.2 gives a p-value between 0.01 and 0.02, matching choice A.
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