Midterm Review Problems

Midterm Review Problems

October 19, 2013

1. Consider the following research title: “Cooperation among nursery school children under two types of instruction.” In this study, what is the inde- pendent variable? What is the dependent variable?

2. Determining a person’s reaction time (in milliseconds) would involve mea- surement on a(n) scale of measurement.

• Interval

• Ratio

• Ordinal

• Nominal

3. True or False? If false, why? If two individuals have different measurements on an ordinal scale, you can tell whose score is higher but you cannot determine how much higher.

4. True or False? If false, why? Nominal variables allow you measure direction between different values of the variable. That is, with a nominal variable, you can tell which value of the variable is “more” or “bigger” than the other.

5. True or False? If false, why? If two individuals have different scores on an interval, you can determine whose score is higher and you can determine how much higher.

6. Pliner and Chaiken (1990) examined the amount of food eaten by male and female participants in the presence of a person of the same gender or a person of the opposite gender. In their study, what was the independent variable? What was the dependent variable?

7. In a manipulation in a true experiment,

a. the researcher manipulates the independent variable b. the researcher manipulates the dependent variable

c. the researcher looks for an effect in the independent variable

d. a and c are correct

e. b and c are correct

8. A variable such as intelligence that cannot be seen or measured directly is know as a(n)

• dummy variable

• experimental control

• construct

• operational definition

9.

X f

8 3

5 4

4 4

3 2

For this table, find

• the total n

• the total proportion of 4 scores

• the total proportion of scores less than or equal to 5

• the percentage of scores more than or equal to 5 10. For the following, use X = 3, 4, 5, 1, 0, 8.

X (X + X) = ?

X (X − 3.5) = ?

P(X − 3.5)

P X = ?

11. Suppose you are competing in a swimming competition. You are asked the following three questions. Your answer to each is given afterward.

(a) What was your participant number? 18.

(b) What place did you finish in? 18.

(c) How many seconds did it take you to swim a lap? 18.

Despite every answer being 18, the answers to each question mean entirely different things. Why?

12. Use Figure 1 to answer the following questions:

2 3 4 5

10 15 20 25 30

Car Weight and Miles per Gallon

Car Weight

Miles P er Gallon

Figure 1: Scatterplot of Car Weight and Mileage (per Gallon)

• What are the measurement scales for the variables in the scatterplot above?

• True or False? If false, why? Given the information provided, it appears there is no relationship between a car’s mileage and its weight.

13. A teacher wishes to know whether the males in his/her class have more conservative attitudes than the females. A questionnaire is distributed assessing attitudes and the males and the females are compared. Is this an example of descriptive or inferential statistics?

14. If we were interested in studying salaries in the National Basketball Asso- ciation, the least useful measure of the typical salary would be

• the mode

• the range

• the median

• the mean

15. True or False? If false, why? The mode must be an actual score that occurred in the data set.

16. We are most likely to randomly pick which score from an actual data set?

• the mode

• the lowest score

• the median

• the highest score

17. When the distribution is symmetric, which of the following are always equal?

• the mode and the mean

• the mode and the median

• the median and the mean

• the mean, median, and mode

18. If a store manager wanted to stock the men’s clothing department with shirts fitting the most men, which measure of central tendency of men’s shirt sizes should be employed?

• the mean

• the median

• the mode

19. The population variance is (a) a biased estimate.

(b) an estimate of the sample variance.

(c) calculated exactly like the sample variance.

(d) usually an unknown that we try to estimate.

20. Which of the following sets of data is likely to have the smallest standard deviation?

(a) The amount that you and your friends pay for college tuition.

(b) The distribution of heights of students in an elementary school.

(c) The distribution of SAT scores for students from your high school.

(d) The grade point averages of students from your high school’s honors biology class.

21. When calculating the standard deviation we divide by N-1 rather than N because the result is

(a) equal to the population mean.

(b) easier to interpret.

(c) smaller.

(d) less biased on average.

22. You would obtain a negative value for the variance if:

(a) the distribution is very negatively skewed.

(b) You would never obtain a negative variance.

(c) all observations were at the mean.

(d) the distribution if positively skewed.

23. The normal distribution is

(a) the distribution that we would expect for the salaries of basketball players.

(b) a distribution with a known shape and other properties.

(c) most frequently observed for the distribution of small sample sizes.

(d) characterized by a high degree of skewness.

24. We know that 25%of the class got an A on the last Homework, and 30%

got a B. What percent got either an A or a B?

(a) We cannot tell from the information that is presented.

(b) 25% · 30% = 7.5 (c) 25% + 30% = 55 (d) 45%

25. A z score of 1.25 represents an observation that is (a) 1.25 standard deviations below the mean.

(b) 0.25 standard deviations above the mean of 1.

(c) none of these choices.

(d) 1.25 standard deviations above the mean.

26. The tables of the standard normal distribution contain only positive values of z. This is because:

(a) we aren’t interested in negative values of z.

(b) probabilities can never be negative.

(c) it would be redundant: the distribution is symmetric, so propor- tion sizes are equal on both the left and right side of the normal distribution.

(d) z can take on only positive values.

27. If we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately

(a) 35-50 (b) 45-55 (c) 30-70 (d) 70-90

28. The difference between a standard score of -1.0 and a standard score of 1.0 is:

(a) the standard score -1.0 is above the mean while 1.0 is below the mean.

(b) the standard score 1.0 is farther from the mean than -1.0.

(c) the standard score -1.0 is farther from the mean than 1.0.

(d) the standard score 1.0 is above the mean while -1.0 is below the mean.

29. The real lower limit and the real upper limit of the interval 40-49 are:

(a) 40 and 50 (b) 40 and 49 (c) 39 and 50 (d) 39.5 and 49.5

30. True or False? If false, why? If the distribution of the ages of people were positively skewed, there are more young people than old people.

31. The onset of eating disorders was shown to occur most often during puberty and during the late teen years in girls. A distribution of the frequencies of onset of eating disorders by age would most likely be

(a) unimodal (b) normal

(c) bimodal (d) all of these.

32. The major difference between an interval and ratio scale is that

(a) with an interval scale you can speak meaningfully about a score of 0.

(b) both scales carry the same level of information.

(c) with a ratio scale you can speak meaningfully about a score of 0.

(d) with an interval scale you know which values represent more of the

quantity.

33. Professor Lowe assigned each of her students a number and selected 20 for her study by using a table of random numbers. Professor Lowe was interested in how the type of feedback received would affect the level of happiness in her students. The students were either praised or insulted and then the levels of happiness were measured by a questionnaire administered at the end of the study. What is the dependent variable of this study?

(a) feedback (b) praise

(c) happiness (d) students

34. Use Figure 2 to answer the following questions:

Quiz Scores

Scores

Frequency

2 3 4 5 6 7 8

0 2 4 6 8

Figure 2: Histogram of Quiz Scores

• True or False? If false, why? In the above graph, the mean is lower than the median.

• True or False? If false, why? Quiz scores should not be displayed

on the x-axis of a histogram. Histograms cannot properly display

frequencies for this type of data.

• True or False? Assuming the quiz is out of 8 points, it appears that most students did fairly well.

35. In a box there are 3 red pens, 5 blue pens, and 2 black pens. If a person selects a pen at random, find the probability that the pen is

• A blue or a red pen.

• A red or a black pen.

36. If we are comparing the adrenaline scores of children who live near an airport with those who live away from an airport, the dependent variable is:

(a) distance from the airport.

(b) location.

(c) stress.

(d) adrenaline.

37. True or False? If false, why? If your score on the SAT placed you in the 80th percentile, this means you did better than 80 percent of the test-takers.

38. What is the relationship between the standard normal distribution and the normal distribution?

(a) The standard normal distribution is just a normal distribution with a mean equal to 0 and a standard deviation equal to 1.

(b) Unlike the standard normal distribution, the normal distribution is not restricted to a predefined mean or standard deviation.

(c) Both a and b.

(d) None of these.

39. Bonus! Seligman, Nolen-Hecksema, Thornton, and Thornton (1990) classified participants in their study (who were members of a university swim team) as Optimists or Pessimists. They then asked them to swim their best event, and in each case they reported times that were longer than the swimmer actually earned. Half an hour later they asked them to repeat the event again. The dependent variable was T ime

/T ime

, so a ratio greater than 1.0 indicates faster times on the second trial. The data follow.

Optimists

0.986 1.108 1.080 0.952 0.998 1.017 1.080

1.026 1.045 0.996 0.923 1.000 1.003 0.934

1.009 1.065 1.053 1.108 0.985 1.001 0.924

0.968 1.048 1.027 1.004 0.936 1.040

Pessimists

0.983 0.947 0.932 1.078 0.914 0.955 0.962 0.944 0.941 0.831 0.936 0.995 0.872 0.997 0.983 1.105 1.116 0.997 0.960 1.045 1.095 0.944 1.069 0.927 0.988 1.015 1.045 0.864

0.982 0.915 1.047

Calculate the mean, variance, and standard deviation for each group (use a calculator). Seligman et al. thought that optimists would try harder after being disappointed. Does it look as if they were correct? Explain your answer.

References

1. David Howell. 2010. Fundamental Statistics for the Behavioural Sciences.

2. David Howell. 2012. Statistical Methods for Psychology.

3. Gravetter and Walnau. 2013. Essentials of Statistics for the Behavioural Sciences.

4. Online Statistics Education – Free E-Book.

5. Allan Bluman. 2005. Probability Demystified.