Question

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

Time	13	10	9	9	2	10	12	8
Score	84	83	90	76	74	86	99	85

x-values   y-values

1. Find the correlation coefficient: r=r=    Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0: ? r ρ μ  == 0
   H1:H1: ? μ ρ r   ≠≠ 0
3. The p-value is:    (Round to four decimal places)
   
4. 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.
   Select an answer At the 5% significance level, the data provides 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. At the 5% significance level, the data provides sufficient 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.
   
5. r2r2 =  (Round to two decimal places)   
   
6. Interpret r2r2 : Select an answer Approximately 40% of the variation in the the amount of time statistics students study per week can be explained by the test scores that student receive Approximately 40% of the variation in the test scores that students receive can be explained by the amount of time statistics students study per week.
   
   
7. e. The equation of the linear regression line is:   
   ˆyy^ =  + xx   (Please show your answers to two decimal places)   
   
8. Use the model to predict the test score for a student who spends 8 hours per week studying. test score =  (Please round your answer to the nearest whole number.)    
   
9. Interpret the slope of the regression line in the context of the question: Select an answer For every additional hour per week students spend studying, they tend to score on averge 1.49 higher on the test. The slope has no practical meaning since you cannot predict what any individual student will score on the final. As x goes up, y goes up.
   
10. Interpret the y-intercept in the context of the question: Select an answer The y-intercept has no practical meaning for this study. The best prediction for a student who doesn't study at all is that the student will score 71 on the test. If a student does not study at all, then that student will score 71 on the test. The average test score is predicted to be 71.

Answer 1

using minitab>stat>correlation

we have

Correlation: Time, score

Pearson correlation of Time and score = 0.631
P-Value = 0.0934

1. Find the correlation coefficient: r=0.63
2. The null and alternative hypotheses for correlation are:
   H0: ρ = 0
   H1: ρ ≠ 0
3. The p-value is:0.0934
4. At the 5% significance level, the data provides sufficient 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.

using minitab/>stat>basic stat>regression

we have

Regression Analysis: score versus Time

The regression equation is
score = 71.05 + 1.488 Time

S = 6.55372 R-Sq = 39.8% R-Sq(adj) = 29.7%

Analysis of Variance

Source DF SS MS F P
Regression 1 170.168 170.168 3.96 0.094
Error 6 257.707 42.951
Total 7 427.875

r² =  0.40

Interpret r2 : Approximately 40% of the variation in the test scores that students receive can be explained by the amount of time statistics students study per week.

e. The equation of the linear regression line is:   
ˆy =71.05 + 1.49 x   (Please show your answers to two decimal places)   

1. Use the model to predict the test score for a student who spends 8 hours per week studying. test score

ˆy =71.05 + 1.49*7 = 81.48~82

1. Interpret the slope :For every additional hour per week students spend studying, they tend to score on averge 1.49 higher on the test.
2. Interpret the y-intercept in the context of the question:If a student does not study at all, then that student will score 71 on the test.