# Testing a Claim about a Difference between Proportions Quiz

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 are the correct hypotheses to test the company's claim? H 0: P A minus P B = 0; H alpha: P A minus P B greater-than 0 H 0: P A minus P B = 0; H alpha: P A minus P B less-than 0 H 0: P A minus P B = 0; H alpha: P A minus P B not-equals 0 H 0: P A minus P B = 0; H alpha: P A minus P B less-than 0

A- H 0: P A minus P B = 0; H alpha: P A minus P B greater-than 0

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, H 0: P A = P B and H alpha: P A greater-than P B? Find the z-table here. 0.11 0.15 0.23 0.46

C- 0.23

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 100 chips from production at plant A and determines that there are 12 defective chips. The specialist then takes a random sample of 100 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 are the correct hypotheses to test the owner's claim? H 0: P A minus P B = 0; H alpha: P A minus P B not-equals 0 H 0: P A minus P B = 0; H alpha: P A minus P B greater-than 0 H 0: P A minus P B = 0; H alpha: P A minus P B less-than 0 H 0: P A minus P B greater-than 0; H alpha: P A minus P B less-than 0

B- H 0: P A minus P B = 0; H alpha: P A minus P B greater-than 0

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 it will land tails up compared to 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 lands tails up and pP = the true proportion of times a penny will land tails up. Which of the following are the correct hypotheses to test the student's claim? H 0: p Upper D minus Upper P p = 0 and H alpha: Upper P Upper D minus Upper P p less-than 0 H 0: p Upper D minus Upper P p greater-than 0 and H alpha: Upper P Upper D minus Upper P p less-than 0 H 0: p D minus P p = 0 and H alpha: P D minus P p not-equals 0 H 0: p D minus P p = 0 and H alpha: P D minus P p greater-than 0

A- H 0: p Upper D minus Upper P p = 0 and H alpha: Upper P Upper D minus Upper P p less-than 0

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. The P-value for this significance test is 0.007. Which of the following is the correct conclusion for this test of the hypotheses H 0: P A minus P B = 0; H alpha: P A minus P B greater-than 0 at the alpha = 0.05 level question mark Researchers should reject the null hypothesis since 0.007 < 0.05. There is sufficient evidence that the true proportion of clothes receiving a rating of 7 or higher is significantly greater for the new formula of detergent. The owner should reject the null hypothesis since 0.007 < 0.05. There is insufficient evidence that the true proportion of clothes receiving a rating of 7 or higher is significantly greater for the new formula of detergent. The owner should fail to reject the null hypothesis since 0.007 < 0.05. There is sufficient evidence that the true proportion of clothes receiving a rating of 7 or higher is significantly greater for the new formula of detergent. The owner should fail to reject the null hypothesis since 0.007 < 0.05. There is insufficient evidence that the true proportion of clothes receiving a rating of 7 or higher is significantly greater for the new formula of detergent.

A- Researchers should reject the null hypothesis since 0.007 < 0.05. There is sufficient evidence that the true proportion of clothes receiving a rating of 7 or higher is significantly greater for the new formula of detergent.

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 random condition is not met. The 10% condition is not met. The Large Counts Condition is not met. All conditions for inference are met.

A- The random condition is not met.

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 shakes the first container, 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 contain 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. The P-value for this significance test is 0.171. Which of the following is the correct conclusion for this test of the hypotheses H Subscript 0 Baseline : P Subscript 1 Baseline minus P Subscript 2 Baseline = 0 and H Subscript alpha Baseline : P Subscript 1 Baseline minus P Subscript 2 Baseline not-equals 0 at the alpha = 0.05 level? The student should reject the null hypothesis since 0.171 > 0.05. There is insufficient evidence that the true proportion of red beads is significantly different between the two containers. The student should fail to reject the null hypothesis since 0.171 > 0.05. There is insufficient evidence that the true proportion of red beads is significantly different between the two containers. The student should reject the null hypothesis since 13 not-equals 16. There is convincing evidence that the true proportion of red beads in container 1 is significantly different from the true proportion of red beads in container 2. The student should fail to reject the null hypothesis since 13 not-equals 16. There is not convincing evidence that the true proportion of red beads in container 1 is significantly different from the true proportion of red beads in container 2.

B- The student should fail to reject the null hypothesis since 0.171 > 0.05. There is insufficient evidence that the true proportion of red beads is significantly different between the two containers.

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 the correct standardized test statistic and P-value for the hypotheses, H 0: P A minus P B = 0 and H alpha: P A minus P B greater-than 0 Find the z-table here. z = StartStartFraction 0.912 minus 0.84 OverOver StartFraction (0.876) (0.124) Over 500 EndFraction EndEndFraction, P-value = 0.014 z = StartStartFraction 0.912 minus 0.84 OverOver StartFraction (0.876) (0.124) Over 250 EndFraction + StartFraction (0.876) (0.124) Over 250 EndFraction EndEndFraction, P-value = 0.007 z = StartStartFraction 0.912 minus 0.84 OverOver StartFraction (0.912) (0.124) Over 250 EndFraction + StartFraction (0.84) (0.16) Over 250 EndFraction EndEndFraction, P-value = 0.007 z = StartStartFraction 0.912 minus 0.84 OverOver StartFraction (0.876) (0.124) Over 250 EndFraction + StartFraction (0.876) (0.124) Over 250 EndFraction EndEndFraction, P-value = 0.014

B- z = StartStartFraction 0.912 minus 0.84 OverOver StartFraction (0.876) (0.124) Over 250 EndFraction + StartFraction (0.876) (0.124) Over 250 EndFraction EndEndFraction, P-value = 0.007

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 shakes the first container, 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 are the correct hypotheses to test the students' claim? H 0: p 1 minus p 2 = 0; H alpha: p 1 minus p 2 greater-than 0 H 0: p 1 minus p 2 = 0; H alpha: p 1 minus p 2 less-than 0 H 0: p 1 minus p 2 = 0; H alpha: p 1 minus p 2 not-equals 0 H 0: p 1 minus p 2 not-equals 0; H 0: p 1 minus p 2 = 0

C- H 0: p 1 minus p 2 = 0; H alpha: p 1 minus p 2 not-equals 0

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, H 0: P A = P B and H alpha: P A greater-than P B? z = StartStartFraction 0.12 minus 0.10 OverOver StartRoot StartFraction (12) (68) Over 80 EndFraction + StartFraction (10) (0.80) Over 90 EndFraction EndRoot EndEndFraction z = StartStartFraction 0.10 minus 0.12 OverOver StartRoot StartFraction (0.15) (0.85) Over 80 EndFraction + StartFraction (0.11) (0.89) Over 90 EndFraction EndRoot EndEndFraction z = StartStartFraction 0.12 minus 0.10 OverOver StartRoot StartFraction (0.13) (0.87) Over 80 EndFraction + StartFraction (0.13) (0.87) Over 90 EndFraction EndRoot EndEndFraction z = StartStartFraction 0.10 minus 0.12 OverOver StartRoot StartFraction (0.13) (0.87) Over 80 EndFraction + StartFraction (0.13) (0.87) Over 90 EndFraction EndRoot EndEndFraction

C- z = StartStartFraction 0.12 minus 0.10 OverOver StartRoot StartFraction (0.13) (0.87) Over 80 EndFraction + StartFraction (0.13) (0.87) Over 90 EndFraction EndRoot EndEndFraction

A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads is the same for both containers. The students believe the proportions are different. Each student shakes the first container, 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 standardized test statistic and P-value for the hypotheses, H 0: p 1 minus p = 0 and H alpha: P A minus P B not-equals 0 Find the z-table here. z = StartStartFraction 0.20 minus 0.32 OverOver StartRoot StartFraction (0.26) (0.74) Over 100 EndFraction EndRoot EndEndFraction, p-value = 0.0855 z = StartStartFraction 0.20 minus 0.32 OverOver StartRoot StartFraction (0.20) (0.80) Over 50 EndFraction EndRoot StartFraction (0.32)(0.68) Over 50 EndFraction EndEndFraction, p-value = 0.171 z = StartStartFraction 0.20 minus 0.32 OverOver StartRoot StartFraction (0.26) (0.74) Over 50 EndFraction EndRoot StartFraction (0.26)(0.74) Over 50 EndFraction EndEndFraction, p-value = 0.171 z = StartStartFraction 0.20 minus 0.32 OverOver StartRoot StartFraction (0.26) (0.74) Over 50 EndFraction EndRoot StartFraction (0.26)(0.74) Over 50 EndFraction EndEndFraction, p-value = 0.0.855

C- z = StartStartFraction 0.20 minus 0.32 OverOver StartRoot StartFraction (0.26) (0.74) Over 50 EndFraction EndRoot StartFraction (0.26)(0.74) Over 50 EndFraction EndEndFraction, p-value = 0.171

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? The random condition is not met. The 10% condition is not met. The Large Counts Condition is not met. All conditions for inference are met.

D- All conditions for inference are met.

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 H 0: P A minus P B = 0 H alpha: P A minus P B greater-than 0 at the alpha = 0.05 level question mark The owner should reject the null hypothesis since 0.225 > 0.05. There is sufficient evidence that the proportion of defective computer chips is significantly greater at plant A. The owner should reject the null hypothesis since 0.225 > 0.05. There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant A. The owner should fail to reject the null hypothesis since 0.225 > 0.05. There is sufficient evidence that the proportion of defective computer chips is significantly greater at plant A. The owner should fail to reject the null hypothesis since 0.225 > 0.05. There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant A.

D- The owner should fail to reject the null hypothesis since 0.225 > 0.05. There is insufficient evidence that the proportion of defective computer chips is significantly greater at plant A.

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? one-proportion t-test two-proportion t-test one-proportion z-test two-proportion z-test

D- two-proportion z-test