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	16	14	15	6	14	15	6
Score	100	89	100	68	99	100	78

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: ? ρ r μ  == 0
   H1:H1: ? μ r ρ   ≠≠ 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 test. 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 test. Thus, the regression line is useful.
   
5. r2r2 =  (Round to two decimal places)   
   
6. Interpret r2r2 : Select an answer Approximately 89% 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 89% 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 7 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 The slope has no practical meaning since you cannot predict what any individual student will score on the testl. As x goes up, y goes up. For every additional hour per week students spend studying, they tend to score on averge 2.81 higher on the test.
   
10. Interpret the y-intercept in the context of the question: Select an answer If a student does not study at all, then that student will score 56 on the test. The average test score is predicted to be 56. The best prediction for a student who doesn't study at all is that the student will score 56 on the test. The y-intercept has no practical meaning for this study.

Answer 1

Sol:

a)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.88

null hypothesis: Ho:               ρ	=	0
Alternate Hypothesis: Ha: ρ	≠	0

test stat t=	r*(√(n-2)/(1-r2))=	4.9583
P value    =		0.0016

p value is less than alpha

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

r² =0.78

There is a large variation in the test 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 78%.

The equation of the linear regression line is: ˆ y =53.56+2.22*x

predicted val=53.557+9*2.217=

73.510 ~ 74

For every additional hour per week students spend studying, they tend to score on average 2.22 higher on the test.

The best prediction for a student who doesn't study at all is that the student will score 54 on the test