Scope of Inference Answers

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.

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?

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.

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?

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?

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 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.

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?

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 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.