A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAS. The results of the survey are shown below. Lovers 4 6 GPA 2.4 1.9 6 2.6 5 5 2.6 2.1 0 3.4 6 6 2 2.3 2.5 3.1 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ?0 The p-value is: Round to 2 decimal places. (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. O There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. O There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. O There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful. O There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate.

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● Question 12
▼
A study was done to look at the relationship between number of lovers college students have had in their
lifetimes and their GPAS. The results of the survey are shown below.
<
Lovers 4 6 6 5 5 0
GPA 2.4 1.9 2.6 2.6 2.1 3.4
20
F3
>
a. Find the correlation coefficient: r =
b. The null and alternative hypotheses for correlation are:
Ho: ?
= 0
H₁: ?0
The p-value is:
d. ² =
e. Interpret ²
c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context
of the study.
6
2
6
2.3 2.5 3.1
(Round to four decimal places)
O There is statistically significant evidence to conclude that a student who has had more lovers
will have a lower GPA than a student who has had fewer lovers.
O There is statistically insignificant evidence to conclude that a student who has had more lovers
I will have a lower GPA than a student who has had fewer lovers.
Round to 2 decimal places.
O There is statistically significant evidence to conclude that there is a correlation between the
number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is
useful.
O There is statistically insignificant evidence to conclude that there is a correlation between the
number of lovers students have had in their lifetimes and their GPA. Thus, the use of the
regression line is not appropriate.
(Round to two decimal places)
288
000
F4
071% of all students will have the average GPA.
O There is a large variation in students' GPAS, but if you only look at students who have had a
fixed number of lovers, this variation on average is reduced by 71%.
O Given any group of students who have all had the same number of lovers, 71% of all of these
studetns will have the predicted GPA.
F5
O There is a 71% chance that the regression line will be a good predictor for GPA based on the
number of lovers a student has had.
F6
MacBook Air
AA
F7
DII
F8
F9
Transcribed Image Text:● Question 12 ▼ A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAS. The results of the survey are shown below. < Lovers 4 6 6 5 5 0 GPA 2.4 1.9 2.6 2.6 2.1 3.4 20 F3 > a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ?0 The p-value is: d. ² = e. Interpret ² c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. 6 2 6 2.3 2.5 3.1 (Round to four decimal places) O There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. O There is statistically insignificant evidence to conclude that a student who has had more lovers I will have a lower GPA than a student who has had fewer lovers. Round to 2 decimal places. O There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful. O There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate. (Round to two decimal places) 288 000 F4 071% of all students will have the average GPA. O There is a large variation in students' GPAS, but if you only look at students who have had a fixed number of lovers, this variation on average is reduced by 71%. O Given any group of students who have all had the same number of lovers, 71% of all of these studetns will have the predicted GPA. F5 O There is a 71% chance that the regression line will be a good predictor for GPA based on the number of lovers a student has had. F6 MacBook Air AA F7 DII F8 F9
O There is statistically insignificant evidence to conclude that a student who has had more lovers
will have a lower GPA than a student who has had fewer lovers.
O There is statistically significant evidence to conclude that there is a correlation between the
number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is
useful.
O There is statistically insignificant evidence to conclude that there is a correlation between the
number of lovers students have had in their lifetimes and their GPA. Thus, the use of the
regression line is not appropriate.
(Round to two decimal places)
d. 2.
e. Interpret ²:
71% of all students will have the average GPA.
O There is a large variation in students' GPAS, but if you only look at students who have had a
fixed number of lovers, this variation on average is reduced by 71%.
80
F3
O Given any group of students who have all had the same number of lovers, 71% of all of these
studetns will have the predicted GPA.
O There is a 71% chance that the regression line will be a good predictor for GPA based on the
number of lovers a student has had.
f. The equation of the linear regression line is:
ŷ =
g. Use the model to predict the GPA of a college student who as had 6 lovers.
(Please round your answer to one decimal place.)
GPA =
(Please show your answers to two decimal places)
h. Interpret the slope of the regression line in the context of the question:
O For every additional lover students have, their GPA tends to decrease by 0.18.
O As x goes up, y goes down.
O The slope has no practical meaning since a GPA cannot be negative.
i. Interpret the y-intercept in the context of the question:
Olf a student has never had a lover, then that student's GPA will be 3.36.
O The average GPA for all students is predicted to be 3.36.
O The best prediction for the GPA of a student who has never had a lover is 3.36.
O The y-intercept has no practical meaning for this study.
000
F4
F5
MacBook Air
F6
F7
DII
F8
F9
Transcribed Image Text:O There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. O There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful. O There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate. (Round to two decimal places) d. 2. e. Interpret ²: 71% of all students will have the average GPA. O There is a large variation in students' GPAS, but if you only look at students who have had a fixed number of lovers, this variation on average is reduced by 71%. 80 F3 O Given any group of students who have all had the same number of lovers, 71% of all of these studetns will have the predicted GPA. O There is a 71% chance that the regression line will be a good predictor for GPA based on the number of lovers a student has had. f. The equation of the linear regression line is: ŷ = g. Use the model to predict the GPA of a college student who as had 6 lovers. (Please round your answer to one decimal place.) GPA = (Please show your answers to two decimal places) h. Interpret the slope of the regression line in the context of the question: O For every additional lover students have, their GPA tends to decrease by 0.18. O As x goes up, y goes down. O The slope has no practical meaning since a GPA cannot be negative. i. Interpret the y-intercept in the context of the question: Olf a student has never had a lover, then that student's GPA will be 3.36. O The average GPA for all students is predicted to be 3.36. O The best prediction for the GPA of a student who has never had a lover is 3.36. O The y-intercept has no practical meaning for this study. 000 F4 F5 MacBook Air F6 F7 DII F8 F9
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