Question

# What is the relationship between the amount of time statistics students study per week and their...

What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below.

 Time Score 9 3 13 5 15 8 5 16 80 75 91 75 93 78 82 91
1. Find the correlation coefficient: r=r=    Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
H0:H0: ? μ r ρ  == 0
H1:H1: ? r ρ μ   ≠≠ 0
The p-value is:    (Round to four decimal places)

3. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
• There is statistically significant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying.
• There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful.
• There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the use of the regression line is not appropriate.
• There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the final exam than a student who spends less time studying.
4. r2r2 =  (Round to two decimal places)
5. Interpret r2r2 :
• There is a 85% chance that the regression line will be a good predictor for the final exam score based on the time spent studying.
• There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 85%.
• 85% of all students will receive the average score on the final exam.
• Given any group that spends a fixed amount of time studying per week, 85% of all of those students will receive the predicted score on the final exam.
6. The equation of the linear regression line is:

r = 0.92

Hypothesis test:

n = 8

t = 5.75

df = n-2

= 6

p-value = 0.00121

Since p-value = 0.00121 < 0.05 i.e. we can reject H0.

Conclusion:

There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on the final exam. Thus, the regression line is useful.

r2 = 0.8464

There is a large variation in the final exam scores that students receive, but if you only look at students who spend a fixed amount of time studying per week, this variation on average is reduced by 85%.

= 70.205 + 1.397*x

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