Question

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	9	3	13	5	15	8	5	16
Score	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:   
   ˆyy^ =  + xx   (Please show your answers to two decimal places)

Answer 1

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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