Problem 6SE

Are answer keys to multiple-choice tests generated randomly, or are they constructed to make it less likely for the same answer to occur twice in a row? This question was addressed in the article “Seek Whence: Answer Sequences and Their Consequences in Key- Balanced Multiple-Choice Tests” (M. Bar-Hillel and Y. Attali, The American Statistician, 2002:299-303). They studied 1280 questions on 10 real Scholastic Assessment Tests (SATs). Assume that all the questions had five choices (in fact 150 of them had only four choices). They found that for 192 of the questions, the correct choice (A, B, C, D, or E) was the same as the correct choice for the question immediately preceding. If the choices were generated at random, then the probability that a question would have the same correct choice as the one immediately preceding would be 0.20. Can you conclude that the choices for the SAT are not generated at random?

a. State the appropriate null and alternate hypotheses.

b. Compute the value of the test statistic.

c. Find the P-value and state your conclusion.

Chapter 3 Notes: ➔ Movement of air as a result of pressure gradients is called wind ➔ The air that comes in to replace outflowing air in high-pressure system comes from higher in the atmosphere ➔ Air pressure is measured in bars and millibars ➔ Pressure-gradient force:winds blow from high to low pressure ➔ Coriolis effect:Objects appear to be deflected as they move across Earth’s surface due to the rotation of Earth ➔ Friction:This works against movement as air masses interact with objects r neighboring air masses that are moving in a different direction ➔ Outward-flowing air around a high-pressure system rotates as a result of the Coriolis effect, resulting in an anticyclone ➔ Changes in latitude and season lead to the diffe