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Chapter 3: Q R3.6. (page 214)

Calculating achievement a study found a strong link between the number of calculators possessed by high school pupils and their arithmetic proficiency, according to the principle of a high school. Based on this study, he decides to buy each student at his school two calculators, hoping to improve their math achievement. Explain the flaw in the principal’s reasoning.

Short Answer

Expert verified

because correlation does not imply causality, we cannot be certain that the number of calculators owed is the cause of the higher math scores.

Step by step solution

01

Given information

A study found a strong link between the number of calculators possessed by high school pupils and their arithmetic proficiency, according to the principal of a high school.

02

Explanation

If there is a strong correlation between the number of calculators owned by higher students and their math achievements, then there is a strong correlation between the number of calculators owned by higher students and their math achievements. However, because correlation does not imply causality, we cannot be certain that the number of calculators owed is the cause of the higher math scores.

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Most popular questions from this chapter

By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is

a. greater than zero.

b. less than zero.

c. 0.93.

d. 6.4.

e. Can’t tell without seeing the data.

The scatterplot shows the relationship between the number of people per television set and the number of people per physician for 40 countries, along with the least-squares regression line. In Ethiopia, there were 503 people per TV and 36,660 people per doctor. Which of the following is correct?

a. Increasing the number of TVs in a country will attract more doctors.

b. The slope of the least-squares regression line is less than 1.

c. The correlation is greater than 1.

d. The point for Ethiopia is decreasing the slope of the least-squares regression line.

e. Ethiopia has more people per doctor than expected, based on how many people it has per TV.

What’s my grade? In Professor Friedman’s economics course, the correlation

between the students’ total scores prior to the final examination and their final exam scores is r = 0.6. The pre-exam totals for all students in the course have a mean of 280 and a standard deviation of 30. The final exam scores have a mean of 75 and a standard deviation of 8. Professor Friedman has lost Julie’s final exam but knows that her total before the exam was 300. He decides to predict her final exam score from her pre-exam total.

a. Find the equation for the least-squares regression line Professor Friedman should use to make this prediction.

b. Use the least-squares regression line to predict Julie’s final exam score.

c. Explain the meaning of the phrase “least squares” in the context of this question.

d. Julie doesn’t think this method accurately predicts how well she did on the final exam. Determine r2. Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.

One child in the Mumbai study had height 59 cm and arm span 60 cm. This child’s residual is

a. −3.2 cm.

b. −2.2 cm.

c. −1.3 cm.

d. 3.2 cm.

e. 62.2 cm.

A carpenter sells handmade wooden benches at a craft fair every week. Over the past year, the carpenter has varied the price of the benches from \(80

to \)120 and recorded the average weekly profit he made at each selling price. The prices of the bench and the corresponding average profits are shown in the table.

a. Make a scatterplot to show the relationship between price and profit.

b. The correlation for these data is r=0Explain how this can be true even though there is a strong relationship between price and average profit.
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