Which of the following scenarios is most likely to involve dependent samples ($\mathrm{matched} \mathrm{pairs}$)?

When testing the difference of means for paired data, which of the following is the correct null hypothesis?

Which of the following is an example of a dependent sample suitable for analysis with the $t$-test?

Two samples are $————————————$ if the sample values are paired.

Which of the following situations is a matched pairs $t$ test not an appropriate way to analyze?

"[DATA] Does Octane Matter? Octane is a measure of how much fuel can be compressed before it spontaneously ignites. Some people believe that higher-octane fuels result in better gas mileage for their cars. To test this claim, a researcher randomly selected 11 individuals (and their cars) to participate in the study. Each participant received 10 gallons of gas and drove his or her car on a closed course that simulated both city and highway driving. The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine whether the car was filled up with 87-octane or 92-octane fuel first, and the driver did not know which type of fuel was in the tank. The results are in the following table:

d. The differences are computed as “92 octane minus 87 octane.” The normal probability plot of the differences is shown in the next column. The correlation between the differenced data and the expected z-scores is 0.966. Is there reason to believe that the differences are normally distributed? Conclude that the differences can be normally distributed even though the original data are not.

[DATA] Putting It Together: Glide Testing You are a passenger in a single-propeller-driven aircraft that experiences engine failure in the middle of a flight. The pilot wants to maximize the distance that the plane can glide to increase the likelihood of finding a safe place to land. To accomplish this goal, should the pilot allow the propeller to “windmill” or should the pilot force the propeller to stop? To obtain the data needed to answer the research question, a pilot climbed to 8000 feet at a speed of 60 knots and then killed the engine with the propeller either windmilling or stopped. Because the time to descend is directly proportional to glide distance, the time to descend to 7200 feet was recorded in seconds and used as a proxy for glide distance. The design called for randomly choosing the order in which the propeller would windmill or be stopped. The data in the table represent the time to descend 800 feet for each of 27 trials. Note: Visit www.aceaerobaticschool.com to see footage of this scenario.

c. Explain why blinding is not possible for this experiment.