Chapter 3 AP Stats Review

Other things being equal, larger automobile engines are less fuel-efficient. You are planning an experiment to study the effect of engine size (in liters) on the fuel efficiency (in miles per gallon) of sport utility vehicles. In this study,

• gas mileage is a response variable, and you expect to find a negative association.

• gas mileage is a response variable, and you expect to find a positive association.

• gas mileage is an explanatory variable, and you expect to find a strong negative association.

• gas mileage is an explanatory variable, and you expect to find a strong positive association.

• gas mileage is an explanatory variable, and you expect to find very little association.

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

• 85.5

• 90

• 9

• 95.5

• none of these

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?

• –2.0

• 2.0

• 3.0

• 93

• none of these

The correlation between the heights of fathers and the heights of their (fully grown) sons is r = 0.52. This value was based on both variables being measured in inches. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

• much smaller than 0.52

• slightly smaller than 0.52

• unchanged: equal to 0.52

• slightly larger than 0.52

• much larger than 0.52

All but one of the following statements contains an error. Which statement could be correct?

• There is a correlation of 0.54 between the position a football player plays and his weight.

• We found a correlation of r = –0.63 between gender and political party preference.

• The correlation between the distance travelled by a hiker and the time spent hiking is r = 0.9 meters per second.

• We found a high correlation between the height and age of children: r = 1.12.

• The correlation between mid-August soil moisture and the per-acre yield of tomatoes is r = 0.53.

A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is y-hat= 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements must be true?

• For each one-point increase in performance rating, the raise will increase on average by $1400.

• The actual relationship between salary raises and performance rating is linear.

• The residuals for half the observations in the dataset will be positive.

• The correlation between salary raise and performance rating is negative.

• If the mean performance rating is 1.2, then the mean raise is $3800.

A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model?

• A residual plot is not an appropriate means for evaluating a linear model.

• The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players.

• The curved pattern in the residual plot suggests that the linear model is not appropriate.

• There are not enough data points to draw any conclusions from the residual plot.

• The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: Which of the following is correct?

• If the UV value increases by 1 Dobson unit, the yield is expected to increase by 0.0463 kg.

• If the yield increases by 1 kg, the UV value is expected to decrease by 0.0463 Dobson units.

• If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg.

• The predicted yield is 4.3 kg when the UV value is 20 Dobson units.

• None of the above is correct.

Which of the following statements about the slope of the least-squares regression line is true? 

• It has the same sign as the correlation coefficient r.
• The square of the slope equals the proportion of the variation in the response variable that is explained by the explanatory variable.
• It is unitless.
• When the x-variable is 0, this is what the y-variable is predicted to be.

A study showed that students who spend more time studying for statistics tests tend to achieve better scores on their tests. In fact, the number of hours studied turned out to explain 81% of the observed variation in test scores among the students who participated in the study. What is the value of the correlation between number of hours studied and test score? 

• r = 0.81
• r = 0.656
• r = 0.9
• There is no way to know.