Multiple Choice Questions Correlation

1. A research study has reported that there is a correlation of r = −0.59 between the eye color (brown, green, blue) of an experimental animal and the amount of nicotine that is fatal to the animal when consumed. This indicates: (a) nicotine is less harmful to one eye color than the others. (b) the lethal dose of nicotine goes down as the eye color of the animal changes. (c) one must always consider the eye color of animals in making statements about the effect of nicotine consumption. (d) the researchers need to do further study to explain the causes of this negative correlation. (e) the researchers need to take a course in statistics because correlation is not an appropriate measure of association in this situation. Solution: e - correlation cannot be computed with nominal variables Past performance 1997 Jun - 98% 2. If the correlation between body weight and annual income were high and positive, we could conclude that: (a) high incomes cause people to eat more food. (b) low incomes cause people to eat less food. (c) high income people tend to spend a greater proportion of their income on food than low income people, on average. (d) high income people tend to be heavier than low income people, on average. (e) high incomes cause people to gain weight. Solution: d Past performance 1991 Dec - 70% (c-25%) Past performance 1993 Apr - 75% (c-25%)

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3. A study found a correlation of r = −0.61 between the sex of a worker and his or her income. You conclude that: (a) women earn more than men on average. (b) women earn less than men on average. (c) an arithmetic mistake was made; this is not a possible value of r. (d) this is nonsense because r makes no sense here. (e) the correlation of −0.61 is not meaningful here because the relationship between sex and income is likely nonlinear. Solution: d Past performance 1993 Feb - 60% (e-33%) 4. A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties A and B are represented by x’s and o’s, respectively, in the following plot:

Which of the following statements is FALSE? (a) Considering variety A alone, there is a negative correlation between sepal length and sepal width. (b) Considering variety B alone, the least squares regression line for predicting sepal length from sepal width has a negative slope. (c) Considering both varieties together, there is a positive correlation between sepal length and sepal width. (d) Considering each variety separately, there is a positive correlation between sepal length and sepal width. (e) Considering both varieties together, the least squares regression line for predicting sepal length from sepal width has a positive slope. Solution: d

c

2006 Carl James Schwarz

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5. From tax records, it is relative easy to determine the amount of liquor consumed per capita and the number of cigarettes consumed per capita for each of the 10 provinces of Canada. These are plotted on a scatter plot and a high positive correlation is found. Which of the following is correct? (a) This implies that heavy smoking causes people to drink more. (b) This implies that heavy drinking causes people to smoke more. (c) We cannot conclude cause and effect, but this also implies that there is a high positive correlation between cigarette smoking and alcohol consumption for individuals. (d) This could be an example of a correlation caused by a common cause because both activities are highly correlated with average family income and average income varies widely among the provinces. (e) We cannot conclude cause and effect, but this also implies that the same individuals both smoke and consume liquor. Solution: d Past performance 1993 Feb - 44% (c-44%; e-10%) 6. The correlation coefficient provides: (a) a measure of the extent to which changes in one variable cause changes in another variable. (b) a measure of the strength of the linear association between two categorical variables. (c) a measure of the strength of the association (not necessarily linear) between two categorical variables. (d) a measure of the strength of the linear association between two quantitative variables. (e) a measure of the strength of the linear association between a quantitative variable and a categorical variable. Solution: d 7. On May 11th, 50 randomly selected subjects had their systolic blood pressure (SBP) recorded twice – the first time at about 9:00 a.m. and the second time at about 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect: (a) the correlation to be near zero, as the morning and afternoon readings should be independent of one another.

c

2006 Carl James Schwarz

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(b) the correlation to be high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon. (c) the correlation to be high and negative, as those with relatively high readings in the morning will tend to have relatively low readings in the afternoon. (d) the correlation to be near zero, as correlation measures the strength of the linear association. (e) the correlation to be near zero, as blood pressure readings should follow approximately a normal distribution. Solution: b Past performance 1996 Dec - 62% (23%-d) Past performance 1998 Oct - 68% 8. Men tend to marry women who are slightly younger than themselves. Suppose that every man married a woman who was exactly .5 of a year younger than themselves. Which of the following is CORRECT? (a) The correlation is −.5. (b) The correlation is .5. (c) The correlation is 1. (d) The correlation is −1. (e) The correlation is 0 Solution: c - Draw a scatterplot of various aged men and their wives Past performance 2006 Oct - 75% (10%-e)

c

2006 Carl James Schwarz

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