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 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 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 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?

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?

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 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 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 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 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.

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?