Chapter 7 AP Stats

A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be –1.08. On the basis of this you would tell the college that

• the entrance exam is a good predictor of success

• the exam is a poor predictor of success

• students who do best on this exam will be poor students

• students at this school are underachieving

• the college should hire a new statistician (like Mr. Z)

You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. “Least-squares” refers to

• Minimizing the sum of the squares of the 25 houses’ heating costs.

• Minimizing the sum of the squares of the number of rooms in each of the 25 houses.

• Minimizing the sum of the products of each house’s actual heating costs and the predicted heating cost based on the regression equation.

• Minimizing the sum of the squares of the difference between each house’s heating costs and number of rooms.

• Minimizing the sum of the squares of the residuals.

If bivariate data set A has correlation r = 0.95, and a second bivariate data set B has correlation r = –0.95, then

• a linear model does a better job of describing the relationship between the variables in data set A than in data set B.

• a linear model does a better job of describing the relationship between the variables in data set B than in data set A.

• a linear model is the best description of the relationship between the variables in both data set A and data set B.

• you can’t tell whether either data set is best described by a linear model until you examine the scatterplots.

• a mistake has been made—r cannot be negative.

A copy machine dealer has data on the number of copy machines x at each of 89 customer locations and the number of service calls in a month y at each location. Summary calculations give x̅= 8.4, sx= 2.1, y̅= 14.2, sy= 3.8, and r = 0.86. What is the slope of the least-squares regression line of number of service calls on number of copiers?

• 0.86

• 1.56

• 0.48

• 2.82

• cannot tell from the information given

Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

• a straight line is not a good model for the data

• the correlation must be 0

• the correlation must be positive

• outliers must be present

• The regression line might or might not be a good model for the data, depending on the extent of the curve.

What % of the area in a Normal curve is within 1 standard deviation of the mean?

• 50%

• 68%

• 95%

• 99.7%

What % of the Normal curve is greater than 1 standard deviation above the mean?

• 68%

• 34%

• 16%

• 5%

Again, assume the test scores follow the model N(82,5). What score would equate to z = 1.6?

• 90

• 83.6

• 87.6

• 74

Again, assume the test scores follow the model N(82,5). What percent of the scores fall below 82?

• 68%

• 50%

• 34%

• 95%

Again, assume the test scores follow the model N(82,5). What percent of the students scored below a 75?

• 8%

• 5%

• less than 1%

• 1.4%