Testing a Claim about a Difference between Proportions Answers

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?

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following is the correct P-value for the hypotheses, ?Find the z-table here.

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following is a correct statement about the conditions for this test?

A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads is the same in each container. The students believe the proportions are different. Each student selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student’s samples contained 13 red beads from the first container and 16 red beads from the second container. Let p1= the true proportion of red beads in container 1 and p2= the true proportion of red beads in container 2. Which of the following is a correct statement for the conditions for this test?

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and = the true proportion of defective chips from plant B. The P- value for this significance test is 0.225. Which of the following is the correct conclusion for this test of the hypotheses

A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads are the same in each container. The students believe the proportions are different. Each student selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student’s samples contained 10 red beads from the first container and 16 red beads from the second container. Let p1 = the true proportion of red beads in container 1 and p2= the true proportion of red beads in container 2. Which of the following is the correct name for this test?

The owner of a computer company claims that the proportion of defective computer chips produced at plant A is higher than the proportion of defective chips produced by plant B. A quality control specialist takes a random sample of 80 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 90 chips from production at plant B and determines that there are 10 defective chips. Let pA = the true proportion of defective chips from plant A and pB = the true proportion of defective chips from plant B. Which of the following is the correct standardized test statistic for the hypotheses, ?

In a statistics activity, students are asked to spin a penny and a dime and determine the proportion of times that each lands with tails up. The students believe that since a dime is lighter, it will have a lower proportion of times landing tails up compared with the penny. The students are instructed to spin the penny and the dime 30 times and record the number of times each lands tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times. Let pD= the true proportion of times a dime will land tails up and pP= the true proportion of times a penny will land tails up. Which of the following is the correct name for this test?