Testing a Claim about a Difference between Proportions
Question 9 • AQR_A_IC
A laundry detergent company wants to determine if a new formula of detergent, A, cleans better than the original formula, B. Researchers randomly assign 500 pieces of similarly soiled clothes to the two detergents, putting 250 pieces in each group. After washing the clothes, independent reviewers determine the cleanliness of the clothes on a scale of 1–10, with 10 being the cleanest. The researchers calculate the proportion of clothes in each group that receive a rating of 7 or higher. For detergent A, 228 pieces of clothing received a 7 or higher. For detergent B, 210 pieces of clothing received a rating of 7 or higher. Let pA = the true proportion of clothes receiving a rating of 7 or higher for detergent A and pB = the true proportion of clothes receiving a rating of 7 or higher for detergent B. Which of the following is a correct statement about the conditions for this test?
Answer
A
The random condition is met; the 10% condition is met; and the Large Counts Condition is not met.
B
The random condition is met; the 10% condition does not apply; and the Large Counts Condition is met.
C
The random condition is not met; the 10% condition is met; and the Large Counts Condition is not met.
D
The random condition is not met; the 10% condition does not apply; and the Large Counts Condition is met.
Explanation
The random condition is met because the researchers randomly assigned the clothing pieces to the two detergents. The 10% condition does not apply: this is a randomized experiment, not sampling without replacement from a population. The Large Counts Condition is met because each group has at least 10 successes and 10 failures: A has 228 ratings of 7 or higher and 22 below 7; B has 210 ratings of 7 or higher and 40 below 7.
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