A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below.

1. Movies4 0 6 0 2 5 10 2 10 10 3
2. Books10 8 10 13 10 10 6 10 7 3 12

a. Find the correlation coefficient:r=

Round to 2 decimal places.

b. The null and alternative hypotheses for correlation are:

H0: ? r p= 0

H1: ? r p 0

The p-value is:( )Round to 4 decimal places.

c. Use a level of significance of=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 person who watches more movies will read fewer books than a person who watches fewer movies.
• There is statistically insignificant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the use of the regression line is not appropriate.
• There is statistically significant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the regression line is useful.
• There is statistically significant evidence to conclude that a person who watches fewer movies will read fewer books than a person who watches fewer movies.

d. r2= ( ) (Round to two decimal places)

e. Interpretr2:

• 57% of all people watch about the same number of movies as they read books each year.
• There is a 57% chance that the regression line will be a good predictor for the number of books people read based on the number of movies they watch each year.
• There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 57%.
• Given any fixed number of movies watched per year, 57% of the population reads the predicted number of books per year.

f. The equation of the linear regression line is:

y = ( )+ ( ) x (Please show your answers to two decimal places)

g. Use the model to predict the number of books read per year for someone who watches 8 movies per year.

Books per year = ( ) (Please round your answer to the nearest whole number.)

h. Interpret the slope of the regression line in the context of the question:

• For every additional movie that people watch each year, there tends to be an average decrease of 0.55 books read.
• The slope has no practical meaning since people cannot read a negative number of books.
• As x goes up, y goes down.

i. Interpret the y-intercept in the context of the question:

• The y-intercept has no practical meaning for this study.
• The average number of books read per year is predicted to be 12 books.
• The best prediction for a person who doesn't watch any movies is that they will read 12 books each year.
• If someone watches 0 movies per year, then that person will read 12 books this year.

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

Time 12 6 16 2 8 12 13 13

Score 72 72 87 56 64 90 81 87

a. Find the correlation coefficient:r= ()Round to 2 decimal places.

b. The null and alternative hypotheses for correlation are:

• H0: ? r p= 0
• H1:? r p0
• The p-value is: ()(Round to four decimal places)

c. Use a level of significance of=0.05to 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 thefinal 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 thefinal 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 thefinal exam. Thus, the use of the regression line is not appropriate.
• There is statistically significant evidence to conclude that a student who spends more time studying will score higher on thefinal exam than a student who spends less time studying.

d. r2 ()= (Round to two decimal places)

e. Interpretr2:

• 74% of all students will receive the average score on thefinal exam.
• There is a 74% chance that the regression line will be a good predictor for thefinal exam score based on the time spent studying.
• There is a large variation in thefinal 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 74%.
• Given any group that spends a fixed amount of time studying per week, 74% of all of those students will receive the predicted score on the final exam.

f. The equation of the linear regression line is:

• y = ()+() x(Please show your answers to two decimal places)

g. 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.)

h. Interpret the slope of the regression line in the context of the question:

• As x goes up, y goes up.
• For every additional hour per week students spend studying, they tend to score on average 2.29 higher on thefinal exam.
• The slope has no practical meaning since you cannot predict what any individual student will score on the final.

i. Interpret the y-intercept in the context of the question:

• The y-intercept has no practical meaning for this study.
• If a student does not study at all, then that student will score 53 on thefinal exam.
• The averageexam score is predicted to be 53.
• The best prediction for a student who doesn't study at all is that the student will score 53 on the finalexam.