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 8 4 0 3.3 2.9 2 4 GPA 2.7 2.3 3.4 1.7 2.7 2.5 2.7 a. Find the correlation coefficient: r Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? H1: ? The p-value is: (Round to four decimal places) c. Use a level of significance of a of the study. 0.05 to state the conclusion of the hypothesis test in the context
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
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A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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Question 4
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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
6
6
8
4
GPA
2.7
2.3
3.4
1.7
2.7
3.3 2.9
2.5
2.7
a. Find the correlation coefficient: r =
Round to 2 decimal places.
b. The null and alternative hypotheses for correlation are:
Ho: ? v = 0
H1: ?
The p-value is:
(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.
d. p2 =
(Round to two decimal places)
e. Interpret r2
O 80% of all students will have the average GPA.
hing
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* Week 14: Chapter 12 - Linear Re X
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e. Interpret r2:
O 80% of all students will have the average GPA.
O Given any group of students who have all had the same number of lovers, 80% of all of these
studetns will have the predicted GPA.
O There is a 80% chance that the regression line will be a good predictor for GPA based on the
number of lovers a student has had.
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 80%.
f. The equation of the linear regression line is:
=
r (Please show your answers to two decimal places)
g. Use the model to predict the GPA of a college student who as had 7 lovers.
(Please round your answer to one decimal place.)
GPA =
h. Interpret the slope of the regression line in the context of the question:
O As x goes up, y goes down.
O The slope has no practical meaning since a GPA cannot be negative.
O For every additional lover students have, their GPA tends to decrease by 0.19.
i. Interpret the y-intercept in the context of the question:
O The best prediction for the GPA of a student who has never had a lover is 3.56.
O The average GPA for all students is predicted to be 3.56.
O The y-intercept has no practical meaning for this study.
O If a student has never had a lover, then that student's GPA will be 3.56.
Hint: Helnful Video on the Linear Rearession Line L1
ning
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