Question

1. in a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gas, you expect to see

(a) very little association.
(b) a weak negative association.
(c) a strong negative association.
(d) a weak positive association.
(e) a strong positive association.

1. the following graph plots the gas mileage (in miles per gallon) of various cars from the same model year versus the weight of these cars (in thousands of pounds). the points marked with red dots correspond to cars made in japan. from this plot, we may conclude that

graph of weight vs gas mileage with red dots
(a) there is a positive association between weight and gas mileage for japanese cars.
(b) the correlation between weight and gas mileage for all the cars is close to 1.
(c) there is little difference between japanese cars and cars made in other countries.
(d) japanese cars tend to be lighter in weight than other cars.
(e) japanese cars tend to get worse gas mileage than other cars.

1. if women always married men who were 2 years older than themselves, what would be the correlation between the ages of husband and wife?

(a) 2
(b) 1
(c) 0.5
(d) 0
(e) can’t tell without seeing the data

1. the scatterplot shows reading test scores against iq test scores for 14 fifth-grade children. there is one low outlier in the plot. what effect does this low outlier have on the correlation?

(a) it makes the correlation closer to 1.
(b) it makes the correlation closer to 0 but still positive.
(c) it makes the correlation equal to 0.
(d) it makes the correlation negative.
(e) it has no effect on the correlation.

graph of childs iq vs reading test score with an outlier

1. if we leave out the low outlier, the correlation for the remaining 13 points in the preceding figure is closest to

(a) −0.95.
(b) −0.65.
(c) 0.
(d) 0.65.
(e) 0.95.

recycle and review

1. big diamonds (1.2) here are the weights (in milligrams) of 58 diamonds from a nodule carried up to the earth’s surface in surrounding rock. these data represent a population of diamonds formed in a single event deep in the earth.²⁰

table of diamond weights: 13.8, 3.7, 33.8, 11.8, 27.0, 18.9, 19.3, 20.8, 25.4, 23.1, 7.8, 10.9, 9.0, 9.0, 14.4, 6.5, 7.3, 5.6, 18.5, 1.1, 11.2, 7.0, 7.6, 9.0, 9.5, 7.7, 7.6, 3.2, 6.5, 5.4, 7.2, 7.8, 3.5, 5.4, 5.1, 5.3, 3.8, 2.1, 2.1, 4.7, 3.7, 3.8, 4.9, 2.4, 1.4, 0.1, 4.7, 1.5, 2.0, 0.1, 0.1, 1.6, 3.5, 3.7, 2.6, 4.0, 2.3, 4.5
make a histogram to display the distribution of weight. describe the distribution.

1. fruit fly thorax lengths (2.2) fruit flies are used frequently in genetic research because of their quick reproductive cycle. the length of the thorax (in millimeters) for male fruit flies is approximately normally distributed with a mean of 0.80 mm and a standard deviation of 0.08 mm.²¹

(a) what proportion of male fruit flies have a thorax length greater than 1 mm?
(b) what is the 30th percentile for male fruit fly thorax lengths?

Explanation:

Question 30

As the price of a barrel of oil increases, the cost to produce and distribute gas typically increases, so the retail price of gas also tends to increase. This is a strong positive relationship because the two variables (oil price and gas price) move in the same direction and the relationship is expected to be quite strong (since oil is a major input for gas production). So we expect a strong positive association.

• Option (a): For Japanese cars (red dots), as weight increases, gas mileage seems to decrease (negative association), not positive. Eliminate (a).
• Option (b): The overall scatterplot has a negative trend, and the points are not perfectly linear, so correlation is not close to 1. Eliminate (b).
• Option (c): Japanese cars (red dots) are clustered in the lighter weight and higher gas mileage area, while other cars are in heavier and lower gas mileage, so there is a difference. Eliminate (c).
• Option (d): The red dots (Japanese cars) are in the lower weight (left) side of the plot compared to other cars (black dots), so Japanese cars tend to be lighter. This is correct.
• Option (e): Japanese cars (red dots) have higher gas mileage (higher on the y - axis) than other cars with similar weight, so they get better, not worse, gas mileage. Eliminate (e).

If women always marry men who are 2 years older, then for every woman's age \(x\), the husband's age \(y=x + 2\). This is a perfect linear relationship with a positive slope. The correlation coefficient for a perfect linear relationship is 1 (since all points lie exactly on a straight line with positive slope). Correlation can't be 2 (as correlation ranges from - 1 to 1), 0.5 is for a moderate linear relationship, and 0 is for no linear relationship.

Answer:

(e) a strong positive association.

Question 31