AnswersStatistical ReasoningStatistics as a Problem-Solving Process and the Role of Questioning

Practice Test Answers

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1
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Based on the scatterplot and residual plot, is a linear model appropriate for the growth of stock price?

A
A linear model is not appropriate because the scatterplot shows a clear pattern.
B
A linear model is not appropriate because the residual plot is centered about zero.
C
A linear model is not appropriate because the residual plot shows a clear pattern.
D
A linear model is appropriate because the regression line fits the scatterplot well.
2
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Market researchers were interested in the relationship between the number of pieces in a brick-building set and the cost of a set. Information was collected from a survey and was used to obtain the regression equation widehat y is equal to 0 point 0 8 x plus 1 point 2 0 , where x represents the number of pieces in a set and widehat y is the predicted price (in dollars) of a set. Which statement best describes the meaning of the slope of the regression line?

A
For each increase in the number of pieces by 1 , the predicted price increases by 1 point 2 0 dollars .
B
For each increase in the number of pieces by 1 , the predicted price increases by 0 point 0 8 dollars .
C
For each increase in price by 1 dollars , the predicted number of pieces increases by 1 point 2 0 .
D
For each increase in price by 1 dollars , the predicted number of pieces increases by 0 point 0 8 .
3

Machine engineers are designing a new ice machine for use in restaurants. They notice that designs that use cubes containing higher volumes of water take longer to freeze. What are the explanatory variable and response variable for this relationship?

A
Explanatory variable: time to freeze Response variable: volume of water
B
Explanatory variable: type of restaurant Response variable: time to freeze
C
Explanatory variable: shape of ice Response variable: time to freeze
D
Explanatory variable: volume of water Response variable: time to freeze
4

A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x , and their grade point average (GPA), y He collects data for 15 randomly selected students and determines the value for s was 0.67 Which of the following gives the best interpretation of this value?

A
The typical distance between the observed and predicted GPAs was about 0 point 6 7 points.
B
The typical number of absences for students was about 0 point 6 7 days.
C
The typical distance between the observed and predicted numbers of absences was about 0 point 6 7 days.
D
The typical GPA of a student was about 0 point 6 7 points.
5

Bacteria growth was measured over a one-month period. Scatterplot A displays the number of cells measured over the recorded number of days. Two transformations of the data are shown in the next two graphs. Scatterplot B displays the relationship between the number of days and the natural log of the number of cells of bacteria. Scatterplot C displays the relationship between the natural log of the number of days and the natural log of the number of cells of bacteria. Open image in full-screen view Open image in full-screen view Open image in full-screen view Which model best represents the relationship between the number of days and the number of cells of bacteria?

A
A linear model would best represent the relationship because scatterplot B is fairly linear.
B
A linear model would best represent the relationship because scatterplot A is fairly linear.
C
A power model would best represent the relationship because scatterplot C is fairly linear.
D
An exponential model would best represent the relationship because scatterplot B is fairly linear.
6

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and was used to obtain the regression equation widehat y is equal to negative 0 point 2 2 7 x plus 50 point 4 5 5 , where x represents the price of a bobblehead (measured in dollars) and widehat y is the predicted demand of bobbleheads (in units). Which statement best describes the meaning of the y - intercept of the regression line?

A
When the price of a bobblehead is 0 dollars , the predicted demand is 50 point 4 5 5 units. This interpretation is not meaningful because a bobblehead cannot have a price of 0 dollars .
B
When the demand for bobbleheads is 0 units, the predicted price is 0 dollars .
C
When the demand for bobbleheads is 0 units, the predicted price is 50 point 4 5 5 dollars .
D
When the price of a bobblehead is 0 dollars , the predicted demand is 0 point 2 2 7 units. This interpretation is not meaningful because a bobblehead cannot have a price of 0 dollars .
7

The length (in inches) and weight (in ounces) for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the results are given in the computer output. Open image in full-screen view Which of the following represents the average distance between the actual weight and the predicted weight of the bass?

A
3 point 7 7 1
B
13 point 6 1 0
C
24 point 8 7
D
1 point 8 0
8

The equation of the least-squares regression line is hat y is equal to negative 51 point 0 plus 1 point 4 4 x , where hat y is the time (in minutes) to finish the second half of the race and x is the time (in minutes) to finish the first half. Which shows the residual plot?

A
Image with description A dot plot with the x axis titled First-Half Times in Minutes begins with 105 and ends at 140 with equal intervals of 5, such as 105, 110, 115, 120, 125, 130, 135, and 140. The y axis titled Residual begins with negative 40 and ends at 30 with equal intervals of 10, such as negative 40, negative 30, negative 20, negative 10, 0, 10, 20, and 30. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 105, negative 35, a dot at 115, negative 15; a dot at 115, negative 5; a dot at 120, 12; a dot at 123, negative 5; a dot at 123, 5; a dot at 127, 12; a dot at 130, 18; a dot at 133, negative 5; and a dot at 138, 25.
B
Image with description A dot plot with the x axis titled First-Half Times in Minutes begins with 105 and ends at 140 with equal intervals of 5, such as 105, 110, 115, 120, 125, 130, 135, and 140. The y axis titled Residual begins with negative 30 and ends at 40 with equal intervals of 10, such as negative 30, negative 20, negative 10, 0, 10, 20, 30, and 40. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 105, 11; a dot at 105, 35; a dot at 113, 5; a dot at 113, 15; a dot at 120, negative 11; a dot at 123, negative 3; a dot at 123, 4; a dot at 127, negative 12; a dot at 130, negative 18; and a dot at 137, negative 25.
C
Image with description A dot plot with the x axis titled First-Half Times in Minutes begins with 105 and ends at 140 with equal intervals of 5, such as 105, 110, 115, 120, 125, 130, 135, and 140. The y axis titled Residual begins with negative 20 and ends at 20 with equal intervals of 5, such as negative 20, negative 15, negative 10, negative 5, 0, 5, 10, 15, and 20. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 105, 11; a dot at 115, negative 7; a dot at 115, 2; a dot at 120, negative 16; a dot at 123, 7; a dot at 123, negative 3; a dot at 127, negative 5; a dot at 130, negative 7; a dot at 133, 20; and a dot at 138, negative 4.
D
Image with description A dot plot with the x axis titled First-Half Times in Minutes begins with 105 and ends at 140 with equal intervals of 5, such as 105, 110, 115, 120, 125, 130, 135, and 140. The y axis titled Residual begins with negative 20 and ends at 20 with equal intervals of 5, such as negative 20, negative 15, negative 10, negative 5, 0, 5, 10, 15, and 20. A horizontal line parallel to the x axis starts from the point where y is 0. There is a dot at approximately 105, negative 11; a dot at 115, 7; a dot at 115, negative 2; a dot at 120, 16; a dot at 123, negative 7; a dot at 123, 3; a dot at 127, 5; a dot at 130, 7; a dot at 133, negative 20; and a dot at 138, 4.
9

Which of the following best describes the relationship between the variables in the scatterplot?

A
Those with lower 200 -meter times tend to have longer javelin distances. The relationship is strong.
B
Those with lower 200 -meter times tend to have longer javelin distances. The relationship is moderate.
C
Those with higher 200 -meter times tend to have longer javelin distances. The relationship is strong.
D
Those with higher 200 -meter times tend to have longer javelin distances. The relationship is moderate.
10

Based on the residual plot shown, is a linear model appropriate for using launch angle to predict height?

A
A linear model is appropriate because the residual plot is curved.
B
A linear model is not appropriate because the residual plot shows a clear pattern.
C
A linear model is not appropriate because the y -intercept of the regression equation is negative.
D
A linear model is appropriate because many of the residuals are close to zero.
11

Which scatterplot represents the data?

A
Image with description A scatter plot titled Freezing time (hours) 0.6 to 2.2 on the x-axis and Volume and Freezing Time shows Volume (milliliters) 38 to 56 on the y-axis. The points show an upward trend.
B
Image with description A scatter plot titled Volume and Freezing Time shows Volume (milliliters) 38 to 56 on the x-axis and Freezing time (hours) 0.6 to 2.2 on the y-axis. The points show an upward trend.
C
Image with description A scatter plot titled Volume and Freezing Time shows Volume (milliliters) on the x-axis and Freezing time (hours) on the y-axis. The points show an upward trend.
D
Image with description A scatter plot titled Volume and Freezing Time shows numbers 38 to 56 on the x-axis and numbers 0.6 to 2.2 on the y-axis. The points show an upward trend.
12

Which of the following statements is true, according to the graph?

A
The percentage of preference for each type of book is relatively equal among the different grades of students.
B
The percentage of those preferring fiction and nonfiction is equal among 11th-grade students.
C
The highest percentage of those preferring nonfiction is among 12th-grade students.
D
The lowest percentage of those preferring nonfiction is among 9th-grade students.
13

What is the equation of the least-squares regression line?

A
widehat Bacteria is equal to negative 0 point 0 2 3 plus 4 point 2 0 ln Time
B
the natural log of widehat Bacteria is equal to 2 point 0 7 7 plus 0 point 1 4 2 times Time
C
the natural log of widehat Time is equal to 2 point 0 7 7 plus 0 point 1 4 2 times Bacteria
D
the natural log of widehat Bacteria is equal to 0 point 1 4 2 plus 2 point 0 7 7 times Time
14

Using technology, the slope of the least-squares regression line is

A
negative 0 point 1 0, which means for each additional absence, the GPA is predicted to decrease by 0 point 1 0 points.
B
negative 0 point 1 0, which means for each additional absence, the GPA will decrease by 0 point 1 0 points.
C
0 point 1 0 , which means for each additional absence, the GPA will increase by 0 point 1 0 points.
D
0 point 1 0 , which means for each additional absence, the GPA is predicted to increase by 0 point 1 0 points.
15

What is the residual for the rideshare cost with a distance of 16 miles?

A
5 point 2 1
B
11 point 3 5
C
42 point 4 9
D
2 point 3 3
16

Which of these statements best describes the relationship between the variables shown in the scatterplot?

A
A short stay (under two days) is equally likely for smaller and larger hospitals.
B
There is little association between number of beds and lengths of stay.
C
There is a negative relationship between number of beds and lengths of stay.
D
There is a positive relationship between number of beds and lengths of stay.
17

Which food order had the lowest percentage of customers ordering no drink?

A
soup
B
pasta
C
sandwich
D
salad
18

The equation of the line hat y is equal to negative 14 point 7 plus 1 point 5 9 x is called the least-squares regression line because it

A
minimizes the sum of the squared vertical distances from the points to the line.
B
is least able to make accurate predictions for the data.
C
passes through each data point.
D
maximizes the sum of the squared vertical distances from the points to the line.

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