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 |
9 | 3 | 13 | 5 | 15 | 8 | 5 | 16 |
---|---|---|---|---|---|---|---|---|

Score |
80 | 75 | 91 | 75 | 93 | 78 | 82 | 91 |

- Find the correlation coefficient: r=r= Round to 2 decimal places.
- The null and alternative hypotheses for correlation are:

H0:H0: ? μ r ρ == 0

H1:H1: ? r ρ μ ≠≠ 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 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.
- 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.

- r2r2 = (Round to two decimal places)
- Interpret r2r2 :
- There is a 85% chance that the regression line will be a good predictor for the final exam score based on the time spent studying.
- 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 85%.
- 85% of all students will receive the average score on the final exam.
- Given any group that spends a fixed amount of time studying per week, 85% of all of those students will receive the predicted score on the final exam.

- The equation of the linear regression line is:

ˆyy^ = + xx (Please show your answers to two decimal places)

Answer #1

r = **0.92**

**Hypothesis test:**

n = 8

t = 5.75

df = n-2

= 6

p-value = 0.00121

Since p-value = 0.00121 < 0.05 i.e. we can reject H0.

**Conclusion:**

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.

r2 = 0.8464

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 85%.

= 70.205 + 1.397*x

**Please upvote if you have liked my answer, would be of
great help. Thank you.**

The table below gives the number of hours five randomly selected
students spent studying and their corresponding midterm exam
grades. Using this data, consider the equation of the regression
line, yˆ=b0+b1x, for predicting the midterm exam grade that a
student will earn based on the number of hours spent studying. Keep
in mind, the correlation coefficient may or may not be
statistically significant for the data given. Remember, in
practice, it would not be appropriate to use the regression line...

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.
Movies
5
8
8
8
1
5
5
9
4
Books
6
0
0
0
7
6
3
0
3
Find the correlation coefficient:
r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0: ? r μ ρ ==...

The table below gives the number of hours ten randomly selected
students spent studying and their corresponding midterm exam
grades. Using this data, consider the equation of the regression
line, yˆ=b0+b1xy^=b0+b1x, for predicting the midterm exam grade
that a student will earn based on the number of hours spent
studying. Keep in mind, the correlation coefficient may or may not
be statistically significant for the data given. Remember, in
practice, it would not be appropriate to use the regression line...

A biologist looked at the relationship between number of seeds a
plant produces and the percent of those seeds that sprout. The
results of the survey are shown below.
Seeds Produced
62
41
55
50
47
54
41
63
46
Sprout Percent
54
67.5
63.5
67
59.5
58
65.5
50.5
54
Find the correlation coefficient:
r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0: ? ρ μ r == 0
H1:H1: ? ρ μ r ≠≠ 0...

A teacher is interested in the relationship between the time
spent studying for an exam and exam score. The table lists scores
for 5 students. The value of b0 = 67.91 and the value of b1 = 0.75
Hours studied 5 18 3 15 17 Exam score 63 87 79 72 82 . Step 3 of 6
: Calculate the Sum of Squares Regression (SSR). Round intermediate
values and final answer to two decimal places

The table below gives the number of hours five randomly selected
students spent studying and their corresponding midterm exam
grades. Using this data, consider the equation of the regression
line, yˆ=b0+b1x, for predicting the midterm exam grade that a
student will earn based on the number of hours spent studying. Keep
in mind, the correlation coefficient may or may not be
statistically significant for the data given. Remember, in
practice, it would not be appropriate to use the regression line...

The table below gives the number of hours five randomly selected
students spent studying and their corresponding midterm exam
grades. Using this data, consider the equation of the regression
line, yˆ=b0+b1x, for predicting the midterm exam grade that a
student will earn based on the number of hours spent studying. Keep
in mind, the correlation coefficient may or may not be
statistically significant for the data given. Remember, in
practice, it would not be appropriate to use the regression line...

Question 14
A high school wants to predict her students' score on a midterm
exam y, given the number of hours a student spent studying x1 and
the student's average homework grade x2. She obtains the multiple
regression equation yˆ=−2.662+4.686x1+0.753x2. Predict the midterm
exam score of a student with an average homework grade of 85, who
spent 4 hours studying, rounding to the nearest integer.
Provide your answer below:

A study was done to look at the relationship between number of
vacation days employees take each year and the number of sick days
they take each year. The results of the survey are shown below.
Vacation Days
0
1
4
9
13
13
15
1
6
9
Sick Days
9
12
10
5
5
1
0
6
4
6
Find the correlation coefficient: r=r= Round
to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:? r μ...

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