# Question: You are a passenger in a single propeller driven aircraft that experiences

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.

(a) The trials took place over the course of a few days. However, for each trial, the pilot conducted both windmilling and stopped propeller one right after the other to minimize any impact of a change in weather conditions. Knowing this, explain why this is matched-pair data.

(b) Why does the researcher randomly determine whether to windmill or stop the propeller ﬁrst for each trial?

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

(d) What is the response variable in the study? What are the treatments?

(e) Compute the difference as “difference = stopped − windmilling.” Draw a boxplot of the differenced data. What do you notice?

(f ) From part (b), you should notice that trial 14 results in an outlier. Because our sample size is small, this outlier will have a major effect on any results. The author of the article

indicated that it was possibly a situation in which there was an updraft of wind, causing the plane to take quite a bit longer than normal to fall 800 feet. Explain why this explanation makes it reasonable to eliminate trial 14 from the analysis.

(g) Redraw a boxplot of the data with trial 14 eliminated. Based on the shape of the boxplot, do you believe it is reasonable to proceed with a matched-pair t-test?

(h) The researchers wanted to determine if stopping the propeller resulted in a longer glide distance. Based on this goal, determine the null and alternative hypotheses.

(i) Conduct the appropriate test to answer the researcher’s question.

(j) Write a few sentences outlining your recommendations to pilots who experience engine failure.

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.

(a) The trials took place over the course of a few days. However, for each trial, the pilot conducted both windmilling and stopped propeller one right after the other to minimize any impact of a change in weather conditions. Knowing this, explain why this is matched-pair data.

(b) Why does the researcher randomly determine whether to windmill or stop the propeller ﬁrst for each trial?

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

(d) What is the response variable in the study? What are the treatments?

(e) Compute the difference as “difference = stopped − windmilling.” Draw a boxplot of the differenced data. What do you notice?

(f ) From part (b), you should notice that trial 14 results in an outlier. Because our sample size is small, this outlier will have a major effect on any results. The author of the article

indicated that it was possibly a situation in which there was an updraft of wind, causing the plane to take quite a bit longer than normal to fall 800 feet. Explain why this explanation makes it reasonable to eliminate trial 14 from the analysis.

(g) Redraw a boxplot of the data with trial 14 eliminated. Based on the shape of the boxplot, do you believe it is reasonable to proceed with a matched-pair t-test?

(h) The researchers wanted to determine if stopping the propeller resulted in a longer glide distance. Based on this goal, determine the null and alternative hypotheses.

(i) Conduct the appropriate test to answer the researcher’s question.

(j) Write a few sentences outlining your recommendations to pilots who experience engine failure.

## Answer to relevant Questions

(a) Test whether µ1 ≠ µ2 at the α = 0.05 level of signiﬁcance for the given sample data. (b) Construct a 95% conﬁdence interval about µ1 - µ2. Assume that the populations are normally distributed. Test whether µ1 > µ2 at the α = 0.05 level of signiﬁcance for the given sample data. Assume that the populations are normally distributed. Ramp metering is a trafﬁc engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the trafﬁc ﬂow. The theory is that ramp metering controls the number of cars on the ...Young children require a lot of time. This time commitment cuts into a parent’s leisure time. A sociologist wanted to estimate the difference in the amount of daily leisure time (in hours) of adults who do not have ...A random sample of n1 = 135 individuals results in x1 = 40 successes. An independent sample of n2 = 150 individuals results in x2 = 60 successes. Does this represent sufﬁcient evidence to conclude that p1 < p2 at the α = ...Post your question