Scope of Inference

Question 1

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 randomly assigns 10 to the new additive and 10 to 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.

Revolt · Accepted Answer

C: It can be concluded that the new additive caused the extended life of the cut flowers, and this inference can only be applied to the carnations from the greenhouse.

Question 2

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?

Revolt · Accepted Answer

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.

Question 3

A botanist wants to determine if a fertilizer is effective in the growth of plants. He selects the first 100 plants of the same type of seedling from a greenhouse and assigns the first 50 to the group that uses the fertilizer and remaining seedlings to the group that does not use fertilizer. He makes sure the plants all have the same amount of water, soil, and light for two months. At the end of two months, he measures the heights of the plants and finds that the ones receiving the fertilizer are significantly taller.

Revolt · Accepted Answer

D: Inferences cannot be made for these types of plants, and the conclusion cannot be drawn that the fertilizer will help these types of plants grow taller.

Question 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?

Revolt · Accepted Answer

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.

Question 5

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?

Revolt · Accepted Answer

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.

Question 6

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.

Revolt · Accepted Answer

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.

Question 7

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 randomly selects a ball, not knowing which type is chosen, and hits it. The difference in mean distances traveled (new – original) for the samples was 4.9 feet. Assuming there is no difference in distance traveled between the two types of golf balls, 200 simulated differences in sample means are displayed in the dotplot.

Revolt · Accepted Answer

A: Yes, because a difference in mean distances of 4.9 feet or more occurred only 6 out of 200 times, meaning the difference is statistically significant and there is convincing evidence the new golf ball travels farther than the original golf ball.

Question 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 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?

Revolt · Accepted Answer

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.

Question 9

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?

Revolt · Accepted Answer

D: 40

Question 10

A manufacturer of bottled tea runs a promotion, where 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. Jack really likes the tea and has noticed that the last 10 bottles he has bought has not had a winner. Suspecting the manufacturer’s claim is false, Jack decides to select 10 bottles of tea from 10 randomly selected stores. He is surprised again when none of the 10 bottles is a winner. Assuming the manufacturer’s claim is true, Jack simulates 100 values of selecting winners in 10 bottles. The dotplot displays these simulated proportions.

Revolt · Accepted Answer

A: Yes; because a proportion of 0 occurred 3 out of 100 times, the sample proportion of winners is statistically significant and there is convincing evidence that the manufacturer’s claim is false.

Scope of Inference Answers

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