Scope of Inference

Question 1

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 2

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 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 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.

Revolt · Accepted Answer

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.

Question 4

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 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

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 7

A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 5 carnations placed in the new additive still looked healthy, and 3 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0.2. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot.

Revolt · Accepted Answer

C: No, because a difference in proportions of 0.2 or more occurred 41 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

Question 8

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 seeking 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. They are randomly assigned to two groups, one that takes the new generation of blood pressure medication and one that takes the original medication. At the end of the study, the subjects’ blood pressure and cholesterol levels are measured. The group with the new medication is found to have a significantly lower overall blood pressure than the original medication group. It was also determined that the new medication did not significantly lower cholesterol levels.

Revolt · Accepted Answer

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.

Question 9

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 10

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.

Revolt · Accepted Answer

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.

Scope of Inference Answers

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