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Chapter 4: Problem 102

Suppose that students who scored much lower than the mean on their first statistics test were given special tutoring in the subject. Suppose that they tended to show some improvement on the next test. Explain what might cause the rise in grades other than the tutoring program itself.

Short Answer

Expert verified
Factors other than the tutoring program that might cause a rise in grades are the student's increased personal efforts, change in study habits, increased class participation, and increased familiarity with the course over time.

Step by step solution

01

Identify Individual's Effort

The student probably increased their personal efforts after scoring low on their first test, even outside of the tutoring. This can involve dedicating more time to studying, engaging in group discussions, seeking clarifications on confusing areas or revising more comprehensively.
02

Acknowledge Change in Study Habits

Scoring below the mean could also be a wake-up call for some students to change their study habits. Some may have started to practice daily, revise regularly, or understood the necessity to start preparations well before the test, these changes could hence result in better grades.
03

Consider class Participation

Increased class participation can lead to a better understanding of the subject and hence could be a reason for the scores' improvement. Asking questions, discussing with peers and teachers, or actively participating in class activities can significantly improve comprehension.
04

Factor in the Familiarity with the course over time

With time, students can become more familiar with the teacher's testing style, the nature of the course material, or the textbook's organization. This familiarity can aid students in performing better on subsequent exams.

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Most popular questions from this chapter

The table shows the heights and weights of some people. The scatterplot shows that the association is linear enough to proceed. $$ \begin{array}{|c|c|} \hline \text { Height (inches) } & \text { Weight (pounds) } \\ \hline 60 & 105 \\ \hline 66 & 140 \\ \hline 72 & 185 \\ \hline 70 & 145 \\ \hline 63 & 120 \\ \hline \end{array} $$ a. Calculate the correlation, and find and report the equation of the regression line, using height as the predictor and weight as the response. b. Change the height to centimeters by multiplying each height in inches by \(2.54\). Find the weight in kilograms by dividing the weight in pounds by \(2.205 .\) Retain at least six digits in each number so there will be no errors due to rounding. c. Report the correlation between height in centimeters and weight in kilograms, and compare it with the correlation between the height in inches and weight in pounds. d. Find the equation of the regression line for predicting weight from height, using height in \(\mathrm{cm}\) and weight in \(\mathrm{kg}\). Is the equation for weight (in pounds) and height (in inches) the same as or different from the equation for weight (in \(\mathrm{kg}\) ) and height (in \(\mathrm{cm})\) ?

If there is a positive correlation between number of years studying math and shoe size (for children), does that prove that larger shoes cause more studying of math, or vice versa? Can you think of a confounding variable that might be influencing both of the other variables?

Coefficient of Determination If the correlation between height and weight of a large group of people is \(0.67\), find the coefficient of determination (as a percent) and explain what it means. Assume that height is the predictor and weight is the response, and assume that the association between height and weight is linear.

Suppose a doctor telephones those patients who are in the highest \(10 \%\) with regard to their recently recorded blood pressure and asks them to return for a clinical review. When she retakes their blood pressures, will those new blood pressures, as a group (that is, on average), tend to be higher than, lower than, or the same as the earlier blood pressures, and why?

The table shows some data from a sample of heights of fathers and their sons. The scatterplot (not shown) suggests a linear trend. a. Find and report the regression equation for predicting the son's height from the father's height. Then predict the height of a son with a father 74 inches tall. Also predict the height of a son of a father who is 65 inches tall. b. Find and report the regression equation for predicting the father's height from the son's height. Then predict a father's height from that of a son who is 74 inches tall and also predict a father's height from that of a son who is 65 inches tall. c. What phenomenon does this show? $$ \begin{array}{|c|c|} \hline \text { Father's Height } & \text { Son's Height } \\ \hline 75 & 74 \\ \hline 72.5 & 71 \\ \hline 72 & 71 \\ \hline 71 & 73 \\ \hline 71 & 68.5 \\ \hline 70 & 70 \\ \hline 69 & 69 \\ \hline 69 & 66.5 \\ \hline 69 & 72 \\ \hline 68.5 & 66.5 \\ \hline 67.5 & 65.5 \\ \hline 67.5 & 70 \\ \hline 67 & 67 \\ \hline 65.5 & 64.5 \\ \hline 64 & 67 \\ \hline \end{array} $$
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