Two-Way Tables, Scatter Plots and Correlation: Algebra 1 Math Test – PDF Download

Question 1: Complete a two-way table (2 points)

A coach surveyed 120 students about playing soccer.

1. Complete the row and column totals. (1 point)
2. Find the marginal relative frequency of students who play soccer. (1 point)

Question 2: Compare conditional frequencies (3 points)

The principal recorded how 200 students arrived and whether they were late.

1. Find the joint relative frequency of riding the bus and being late. (1 point)
2. Find the conditional relative frequency of being late for bus riders and for students who do not ride the bus. (1 point)
3. Does the data suggest an association between riding the bus and being late? Justify the answer. (1 point)

Question 3: Describe a scatter plot (2 points)

The scatter plot shows the asking price of eight used laptops of different ages.

1. Describe the direction, strength and form of the association. (1 point)
2. Which value is most likely the correlation coefficient: \(0.98\), \(0.20\), \(-0.20\) or \(-0.98\)? (1 point)

Question 4: Line of fit and prediction (3 points)

A typing class recorded weekly practice time and typing speed for nine students. The line drawn on the scatter plot passes through (2, 30) and (8, 48).

1. Write an equation of the line. (1 point)
2. Interpret the slope in context. (1 point)
3. Predict the typing speed after 10 hours of weekly practice. (1 point)

Question 5: Compute residuals (3 points)

The line \(y=2.5x+8\) is used to model four data points: (2, 15), (4, 17), (6, 26) and (8, 27).

1. Find the predicted value for each point. (1 point)
2. Find the residual for each point. (1 point)
3. Which point lies farthest above the line? (1 point)

Question 6: Interpret a residual plot (2 points)

A student fit a line to a data set and graphed the residuals.

1. Is a linear model appropriate for this data? Explain. (1 point)
2. Describe how the residual plot would look if the line were a good fit. (1 point)

Question 7: Interpret the correlation coefficient (2 points)

A study of students found \(r=-0.84\) between weekly hours of video games and grade point average.

1. Describe the direction and strength of the relationship. (1 point)
2. A second study found \(r=0.31\) between hours of sleep and grade point average. Which study shows the stronger linear relationship? Explain. (1 point)

Question 8: Correlation and causation (2 points)

A fire department finds \(r=0.90\) between the number of fire trucks sent to a fire and the dollar damage the fire causes.

1. Does this show that sending more fire trucks causes more damage? Explain. (1 point)
2. Name a lurking variable that could explain the correlation. (1 point)

Question 9: Extrapolation (1 point)

Using readings from the first 6 hours, a line \(y=-14x+100\) models a phone’s battery percent \(y\) after \(x\) hours of use. Predict the battery percent after 10 hours and decide whether the prediction is reasonable.

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