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 12 0 3 14 14 9 0 13 10 Score 95 60 73 85 86 89 65 97 93 Find the correlation coefficient: r=r=    Round to 2 decimal places. The null and alternative hypotheses for correlation are: H0:H0: ? μ ρ r  == 0 H1:H1: ? ρ μ r   ≠≠ 0 The p-value is:    (Round to four decimal places) 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 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. 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. r2r2 =  (Round to two decimal places) Interpret r2r2 : 79% of all students will receive the average score on the final exam. 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 79%. Given any group that spends a fixed amount of time studying per week, 79% of all of those students will receive the predicted score on the final exam. There is a 79% chance that the regression line will be a good predictor for the final exam score based on the time spent studying. The equation of the linear regression line is:    ˆyy^ =  + xx   (Please show your answers to two decimal places)    Use the model to predict the final exam score for a student who spends 7 hours per week studying. Final exam score =  (Please round your answer to the nearest whole number.)    Interpret the slope of the regression line in the context of the question: 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. For every additional hour per week students spend studying, they tend to score on averge 2.05 higher on the final exam. Interpret the y-intercept in the context of the question: The best prediction for a student who doesn't study at all is that the student will score 65 on the final exam. If a student does not study at all, then that student will score 65 on the final exam. The average final exam score is predicted to be 65. The y-intercept has no practical meaning for this study.

Ho: ρ = 0
Ha: ρ > 0

Find the Linear Correlation Coefficient
r =

Find the p-value
p-value =   

The p-value is

• Less than (or equal to) αα
• Greater than αα

The p-value leads to a decision to

• Accept Ho
• Do Not Reject Ho
• Reject Ho

The conclusion is

• There is a significant linear correlation between advertising expense and profit.
• There is a significant positive linear correlation between advertising expense and profit.
• There is a significant negative linear correlation between advertising expense and profit.
• There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit.

=

Answer 1