Week Two Practice Problems

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Week Two Practice Problems

Prepare a written response to the following questions.

Chapter 2

12. For the following scores, find the mean, median, sum of squared deviations, variance, and standard deviation:

1,112; 1,245; 1,361; 1,372; 1,472

16. A psychologist interested in political behavior measured the square footage of the desks in the official office for four U.S. governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, 36 square feet.

1. Figure the means and standard deviations for the governors and CEOs.
2. Explain, to a person who has never had a course in statistics, what you have done.
3. Note the waus in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.

21. Radel and colleagues (2011) conducted a study of how feeling overly controlled makes you desire—even unconsciously—more freedom. In their study, 52 Canadian undergraduates played a video game in a laboratory and were randomly assigned to either:

1. an automony deprivation condition, in which they were told to follow instructions precisely, constantly given instructions over a loudspeaker, and carefully observed on everything they did.
2. a neutral condition, which was much more laid back.
   

After this activity, they were asked to do a “lexical decision task” (a standard approach for measuring unconscious responses) in which they were shown a series of words and nonwords in random order and had to press “C” if it was a real word or “N” if not. Half of the real words were related to autonomy (e.g., freedom, choice) and half were neutral (e.g., whisper, hammer). The key focus of the study was on how long it took people to press the button *(“response latency”) for each kind of real word, averaged over the many words of each type. The table below shows the mean and standard deviation across the participants of these four categories of results. Thus, for example, 782 milliseconds (thousandths of a second) is the average time it took participants in the autonomy-deprived condition to respond to the autonomy-related words, and 211 is the standard deviation across the 26 participants’ average response time in that condition. Explain the numbers in this table toa person who has never had a course in statistics. (Be sure to explain some specific numbers, as well as the general principle of the mean and standard deviation.) For your interest, the pattern of results shown here supported the researchers’ hypothesis: “Relative to a neutral instructional climate, a controlling climate thwarting the need for autonomy…enhanced accessibility for autonomy-related words.” (p.924).

Chapter 3

14. On a standard measure of hearing ability, the mean is 300 and the standard deviation is 20. Give the raw scores for persons whose Z scores for persons who score 340, 310, and 260. Give the raw scores for persons whose Z scores on this test are 2.4, 1.5, and -4.5.

16. The amount of time it takes to recover physiologically from a certain kind of sudden noise is found to be normally distributed with a mean of 80 seconds and a standard deviation of 10 seconds. Using the 50%–34%–14% figures, approximately what percentage of scores (on time to recover) will be:

Above 100?

Below 100?

Above 90?

Below 90?

Above 80?

Below 80?

Above 70?

Below 70?

Above 60?

Below 60?

18. Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table, what percentage of architects have Z scores:

Above .10?

Below .10?

Above .20?

Below .20?

Above 1.10?

Below 1.10?

Above -.10?

Below -.10?

21. Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.8 feet with a standard deviation of .5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of .6. Both women’s and men’s reach from this position is normally distributed. If this design is implemented:

What percentage of women will not be able to work on this instrument panel?

What percentage of men will not be able to work on this instrument panel?

Explain your answers to a person who has never had a course in statistics.

24. Suppose that you were going to conduct a survey of visitors to your campus. You want the survey to be as representative as possible.

How would you select the people to survey?

Why would that be your best method?

References

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