Ch. 6 Quiz - Correlation

ALL but one of the statements below contains a mistake. Which one could be true?

• The correlations between the time it takes to get ready in the morning and gender is 0.78

• The number of apricots on a tree and the amont of fertilizer has a 1.12 correlation.

• The correlation between the height of a bean plant and the day is 0.78 in/day.

• The correlations between your golf score and the number of hours you practice is -0.36

Answer explanation

Correlation is only between quantitative variables. Gender is categorical.

Correlation must be between -1 and 1, so 1.12 is impossible.

Correlation has no unit so a correlation of 0.78in/day is not correct.

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Which of the statments below contains a mistake?

• A new car owner keeps track of the mileage displayed on the car's instrument panel. as well as the actual mileage by hand. The correlation between the actual mileage and displayed mileage is 0.71

• For a sample of packages, the correlation between weight and shipping time was 0.12.

• In a sample of court cases, the correlation between the race of the defendant and whether or not the defendant was convicted was -0.44.

• The correlation between tail length and weight of cats is 0.67

Answer explanation

Race is not a quantitative variable so correlation calculations are invalid.

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Which of the following relationships are likely to show a negative correlation?

I. The number of minutes third graders spend practicing multiplication and the number of minutes it takes third graders to complete a 50-question multiplication quiz.

II. The speed of a bicycle and the length of the skid mark when the brakes are applied.

• I only

• II only

• Both I and II

• Neither I or II

Answer explanation

Students who study more should finish faster, so less time. This means negative correlation.

A faster bike will leave a longer skid mark. Which means positive correlation.

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All of the pairs of variables below are positively correlated. Which one is unlikely to illustrate a cause-effect relationship?

• The number of pieces in a jigsaw puzzle; the time it takes to assemble the puzzle

• total revenue generated by video arcades in the U.S.; number of computer science doctorates awarded in the U.S.

• number of occupants in a house; annual usage of electricity, measured in kilowatt-hours

• tree diameter; number of board feet of lumber

Answer explanation

Correlation does not equal causation. Just because there is a correlation between Video arcade revenue and computer science doctorates issued in the US doesn't mean they are causing arcades to make sure money.

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Variables X and Y have r = 0.40. If we decrease each X value by 0.1, double each Y value, and then interchange them (put X on the Y- axis and vice versa) the new correlation will be

• -0.40

• 0.15

• 0.40

• 0.60

Answer explanation

If each point is changed in exactly the same way, the correlation is uneffected. This is true if x and y are mismatched also. Correlation remains the same.

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You collect data on the heights and weights (in inches and pounds, respectively) of male elementary school students, and find that the correlation between height and weight is 0.754. After you convert the heights to centimeters and the weights to kilograms, correlation…

• Increases

• Decreases

• Remains the same

• Cannot be determined

Answer explanation

correlation is unchanged by conversion to different units.

Which of the following is not a condition that must be checked before you can use correlation?

• The data must come from a random sample

• Variables must be quantitative

• The scatterplot must show a linear association

• The scatterplot cannot show any outliers

Answer explanation

Scatterplots do not need to come from random samples. It can be intentionally taken.

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What is the correlation of the data shown, to the nearest hundredth? (Approximately)

• 1.00

• 0.96

• -0.96

• -1.00

Answer explanation

1.00 or -1.00 would be a perfect line. Correlation is negative, so -0.96 is best option.

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A negative correlation exists on a scatterplot when…

• values of y remain constant as values of x increase

• values of y change randomly as values of x increase

• values of y increase as values of x increase

• values of y decrease as values of x increase

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Which phrase best represents the relationship between the duration of airline flight in hours and the number of gallons of jet fuel used?

• Correlated, but not causal

• causal, but not correlated

• both correlated and causal

• neither correlated, nor causal

Answer explanation

As a jet flies long, it will obviously consume more gallons of fuel.

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