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 2 5 9 1 4 11 13 11 13 Score 60 61 70 49 72 84 76 80 83 Find the correlation coefficient: r = Round to 2 decimal places. The null and alternative hypotheses for correlation are: H 0 : = 0 H 1 : ≠ 0 The p-value is: (Round to four decimal places) Use a level of significance of α = 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 test than a student who spends less time studying. There is statistically 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. There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher on the test 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 test. Thus, the regression line is useful. r 2 = (Round to two decimal places) Interpret r 2 : There is a 78% chance that the regression line will be a good predictor for the test score based on the time spent studying. Given any group that spends a fixed amount of time studying per week, 78% of all of those students will receive the predicted score on the test. 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%. 78% of all students will receive the average score on the test. The equation of the linear regression line is: ˆ y = + x (Please show your answers to two decimal places) Use the model to predict the test score for a student who spends 9 hours per week studying. Test score = (Please round your answer to the nearest whole number.) Interpret the slope of the regression line in the context of the question: For every additional hour per week students spend studying, they tend to score on average 2.22 higher on the test. The slope has no practical meaning since you cannot predict what any individual student will score on the test. As x goes up, y goes up. Interpret the y-intercept in the context of the question: The average test score is predicted to be 54. The best prediction for a student who doesn't study at all is that the student will score 54 on the test. If a student does not study at all, then that student will score 54 on the test. The y-intercept has no practical meaning for this study.

Answer 1

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