MATH 110 Module 9 Exam Introduction
to Statistics | MATH110 Module 9 Exam
| Questions and Answers Graded A+ |
Portage Learning
Question 1: The Scatterplot and Correlation
A researcher wants to investigate the relationship between the number of hours
students study per week (x) and their final exam score (y). The following data was
collected from a sample of 8 students:
Hours Studied (x) 2 5 1 4 6 3 7 4
Exam Score (y) 65 80 60 75 85 70 95 80
a. Create a scatterplot for the data. (Describe the scatterplot, as you cannot draw
it here).
, b. Based on the scatterplot, describe the direction and strength of the
relationship.
c. Calculate the correlation coefficient (r).
d. Interpret the correlation coefficient you calculated in part (c).
Answer 1:
a. The scatterplot would have the "Hours Studied" on the x-axis and "Exam Score"
on the y-axis. The points would generally follow an upward, linear trend. There are
no obvious outliers.
b. The relationship appears to be positive (as hours increase, exam scores
increase) and strong (the points are clustered closely around an imaginary line).
c.
𝑛∑𝑥𝑦−(∑𝑥)(∑𝑦)
To calculate r, we use the formula: 𝑟 =
√[𝑛∑𝑥 2 −(∑𝑥)2 ][𝑛∑𝑦 2 −(∑𝑦)2 ]
First, we find the necessary sums:
• 𝑛=8
• ∑𝑥 = 2 + 5 + 1 + 4 + 6 + 3 + 7 + 4 = 32
• ∑𝑦 = 65 + 80 + 60 + 75 + 85 + 70 + 95 + 80 = 610
to Statistics | MATH110 Module 9 Exam
| Questions and Answers Graded A+ |
Portage Learning
Question 1: The Scatterplot and Correlation
A researcher wants to investigate the relationship between the number of hours
students study per week (x) and their final exam score (y). The following data was
collected from a sample of 8 students:
Hours Studied (x) 2 5 1 4 6 3 7 4
Exam Score (y) 65 80 60 75 85 70 95 80
a. Create a scatterplot for the data. (Describe the scatterplot, as you cannot draw
it here).
, b. Based on the scatterplot, describe the direction and strength of the
relationship.
c. Calculate the correlation coefficient (r).
d. Interpret the correlation coefficient you calculated in part (c).
Answer 1:
a. The scatterplot would have the "Hours Studied" on the x-axis and "Exam Score"
on the y-axis. The points would generally follow an upward, linear trend. There are
no obvious outliers.
b. The relationship appears to be positive (as hours increase, exam scores
increase) and strong (the points are clustered closely around an imaginary line).
c.
𝑛∑𝑥𝑦−(∑𝑥)(∑𝑦)
To calculate r, we use the formula: 𝑟 =
√[𝑛∑𝑥 2 −(∑𝑥)2 ][𝑛∑𝑦 2 −(∑𝑦)2 ]
First, we find the necessary sums:
• 𝑛=8
• ∑𝑥 = 2 + 5 + 1 + 4 + 6 + 3 + 7 + 4 = 32
• ∑𝑦 = 65 + 80 + 60 + 75 + 85 + 70 + 95 + 80 = 610
