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

Time	14	14	4	3	1	15	11	12	2
Score	81	91	56	71	64	98	74	85	48

1. Find the correlation coefficient: r=r= Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are: H0:H0: ? r = 0 H1:H1: ? r 0 The p-value is: ________ (Round to four decimal places)
3. Use a level of significance of=0.05=0.05to state the conclusion of the hypothesis test in the context of the study. Choose an option
   • a. There is statistically insignificant evidence to conclude that a student who spends more time studying will score higher than a student who spends less time studying.
   • b. There is statistically significant evidence to conclude that a student who spends more time studying will score higher than a student who spends less time studying.
   • c. There is statistically significant evidence to conclude that there is a correlation between the time spent studying and the score on. Thus, the regression line is useful.
   • d. There is statistically insignificant evidence to conclude that there is a correlation between the time spent studying and the score. Thus, the use of the regression line is not appropriate.
4. r2r2= (Round to two decimal places)
5. Interpretr2r2 : Choose an option
   • a. 77% of all students will receive the average score.
   • b. Given any group that spends a fixed amount of time studying per week, 77% of all of those students will receive the predicted score.
   • c. There is a 77% chance that the regression line will be a good predictor for the final score based on the time spent studying.
   • d. There is a large variation in the 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 77%.

• 6. The equation of the linear regression line is: y^ = ___________ + x_________________ (Please show your answers to two decimal places)
  • Use the model to predict the final score for a student who spends 9 hours per week studying. Final score = _____________ (Please round your answer to the nearest whole number.)
  • Interpret the slope of the regression line in the context of the question: Choose an option
    • a. As x goes up, y goes up.
    • b. For every additional hour per week students spend studying, they tend to score on average 2.47 higher.
    • c. The slope has no practical meaning since you cannot predict what any individual student will score.
  • 7. Interpret the y-intercept in the context of the question: Choose an option
• a. If a student does not study at all, then that student will score 53.
• b. The best prediction for a student who doesn't study at all is that the student will score 53.
• c. The y-intercept has no practical meaning for this study.
• d. The average score is predicted to be 53.