AnswersNC-Math 4 CRExperimental Designs

Scope of Inference Answers

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A florist wants to determine if a new additive would extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations from the ones recently delivered by the greenhouse and places the first 10 in water with the new additive and remaining 10 in water with the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The proportion of healthy carnations with the new additive was significantly greater than the proportion of healthy carnations with the original additive.

A
Conclusions about cause and effect for the additives can be made, because the florist randomly selected the 20 carnations; additionally, inferences can be made about the population of carnations at the greenhouse.
B
Conclusions about cause and effect for the additives cannot be made, because the florist did not randomly assign the 20 carnations; however, inferences can be made about the population of carnations at the greenhouse, because the sample was random.
C
Conclusions about cause and effect for the additives can be made, because the florist took a random sample of 20 carnations; however, inferences cannot be made about the population of carnations at the greenhouse, because the carnations were not randomly assigned to the treatments.
D
Conclusions about cause and effect for the additives cannot be made, because the florist took a random sample of 20 carnations; and, inferences cannot be made about the population of carnations at the greenhouse, because the carnations were not randomly assigned to the treatments.
2
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A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company’s previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company’s production line on a specific day. A golf pro then randomly selects a ball, not knowing the type of ball, and hits it. The distance the ball travels is then measured. He continues this procedure until all 80 of the golf balls are hit. At the end of the session, the mean distance traveled for the new type of golf ball was found to the significantly greater than the mean distance for the original-style golf ball.

A
Inferences can be made about all the golf balls produced on that day, and the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
B
Inferences can be made about all the golf balls produced on that day; however, a conclusion cannot be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
C
Inferences cannot be made about all the golf balls produced on that day; and a conclusion cannot be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
D
Inferences cannot be made about all the golf balls produced on that day; however, the conclusion can be made that the new type of golf balls travel farther than the original type of golf ball for this golf pro.
3

A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be –2.3. Assuming there is no difference in the two detergents, 200 simulated differences in sample means are displayed in the dotplot.Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?

Question illustration
A
Yes, because a difference in mean rating of –2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that A is more effective than B.
B
Yes, because a difference in mean rating of –2.3 or less occurred only 5 out of 200 times, meaning the difference is statistically significant, and there is convincing evidence that B is more effective than A.
C
No, because a difference in mean rating of –2.3 or more occurred 195 out of 200 times, meaning the difference is not statistically significant, and there is not convincing evidence that one brand is better than the other.
D
No, because a difference in mean rating of –2.3 or less only occurred 5 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
4

Manufacturers of tires report that tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 52,000 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot.Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage?

Question illustration
A
Yes, because a mean mileage of 52,000 or more occurred only 7 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
B
Yes, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
C
No, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
D
No, because a mean mileage of 52,000 or more occurred 7 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
5

In an activity, students are pulling marbles from a large jar containing blue and red marbles. In their sample, students will calculate the proportion of red marbles. Which of the following sample sizes will have the smallest sampling variability?

A
10
B
20
C
30
D
40
6

A pharmaceutical company develops a new generation of blood pressure medication that may also help with cholesterol. The research and development department advertises in the local papers and online for volunteers who already take blood pressure medication to participate in a study for the new medication. Two hundred people volunteer, and their current blood pressure along with their cholesterol levels are measured. The first 100 volunteers are assigned to the new generation of blood pressure medication, and the next 100 are assigned to the original medication. At the end of the study, the subjects’ blood pressures and cholesterol levels are measured. The group with the new medication is found to have significantly lower overall blood pressure than the original medication group. It was also determined that the new medication did not significantly lower cholesterol levels.

A
Inferences can be made about all blood pressure patients, and the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
B
Inferences can be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
C
Inferences cannot be made about all blood pressure patients, and the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
D
Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
7

A teacher tells her students that a large jar of marbles contains 55% red marbles. Students randomly select a sample of 40 marbles and determined the proportion of red marbles. One sample contained 18 red marbles. Assuming the teacher’s claim is true, 100 simulated proportions are displayed in the dotplot.Using the dotplot and sample proportion, is there convincing evidence that the teacher’s claim is false?

Question illustration
A
Yes, because a proportion of 0.45 or more occurred 87 out of 100 times, the sample proportion of red marbles is statistically significant and there is convincing evidence that the teacher’s claim is false.
B
Yes, because a proportion of 0.45 or less occurred only 16 out of 100 times, the sample proportion of red marbles is statistically significant and there is convincing evidence that the teacher’s claim is false.
C
No, because a proportion of 0.45 or more occurred 87 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher’s claim is false.
D
No, because a proportion of 0.45 or less occurred 16 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher’s claim is false.
8

A consumer agency wants to determine which of two laundry detergents, A or B, cleans better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A, and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale of 1–10, with 1 being the least clean to 10 being the most clean. The mean rating for detergent A is found to be significantly less than the mean rating for detergent B.

A
Inferences can be made about the population of fabric from which the pieces were chosen, and the conclusion can be made that detergent B cleans better than detergent A for all fabric.
B
Inferences cannot be made about the population of fabric from which the pieces were chosen; however, the conclusion can be made that detergent B cleans better that detergent A for these 50 pieces of fabric.
C
Inferences can be made about the population of fabric from which the pieces were chosen; however, the conclusion cannot be made that detergent B cleans better than detergent A for these 50 pieces of fabric.
D
Inferences cannot be made about the population of fabric from which the pieces were chosen; and the conclusion cannot be made that detergent B cleans better than detergent A for these 50 pieces of fabric.
9

A manufacturer of bottled tea runs a promotion in which consumers can win a free bottle of tea if the cap of the bottle says "Winner.” The manufacturer claims that 1 in 5 bottles is a winner. A store owner notices that several of the first bottles of tea sold were winners. Suspecting the manufacturer’s claim is false, the store owner decides to randomly select 10 bottles of tea from the next shipment from the manufacturer. She is again surprised when 4 of the bottles are winners. Assuming the manufacturer’s claim is true, she simulates 100 values of selecting winners in 10 bottles. The dotplot displays these simulated proportions.

Question illustration
A
Yes, because a proportion of 0.4 or more occurred 25 out of 100 times, the sample proportion of winners is statistically significant and there is convincing evidence that the manufacturer’s claim is false.
B
Yes, because a proportion of 0.4 or less occurred 75 out of 100 times, the sample proportion of winners is statistically significant and there is convincing evidence that the manufacturer’s claim is false.
C
No, because a proportion of 0.4 or more occurred 25 out of 100 times, the sample proportion of winners is not statistically significant and there is not convincing evidence that the manufacturer’s claim is false.
D
No, because a proportion of 0.4 or less occurred 75 out of 100 times, the sample proportion of winners is not statistically significant and there is not convincing evidence that the manufacturer’s claim is false.
10

A teacher tells her students that a large jar of marbles contains 55% red marbles. Students randomly select a sample of 40 marbles and determined the proportion of red marbles. One sample a student selected contained 16 red marbles. Assuming the teacher’s claim is true, 100 simulated proportions are displayed in the dotplot.Using the dotplot and sample proportion, is there convincing evidence that the teacher’s claim is false?

Question illustration
A
Yes, because a proportion of 0.40 or more occurred 98 out of 100 times, the sample proportion of red marbles is statistically significant and there is convincing evidence that the teacher’s claim is false.
B
Yes, because a proportion of 0.40 or less occurred only 2 out of 100 times, the sample proportion of red marbles is statistically significant and there is convincing evidence that the teacher’s claim is false.
C
No, because a proportion of 0.40 or more occurred 98 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher’s claim is false.
D
No, because a proportion of 0.40 or less occurred 2 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher’s claim is false.

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Scope of Inference Answers — NC-Math 4 CR