A particular study investigated the use of punishment in cooperation games. In the study, college students repeatedly played a version of the game "prisoner's dilemma," and the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player. Complete parts a through c below using a significance level of
alphaαequals=0.100.10.
Question content area bottom
Part 1
a. Give the null and alternative hypotheses for testing whether average payoff and punishment use are
nothingcorrelatedcorrelated.
Upper H 0H0:
▼
muμ
sigmaσ
rhoρ
beta 1β1
▼
not equals≠
greater than>
less than<
equals=
enter your response here
Upper H Subscript aHa:
▼
sigmaσ
beta 1β1
muμ
rhoρ
▼
less than<
greater than>
equals=
not equals≠
enter your response here
(Type integers or decimals. Do not round.)
Part 2
b. The test, part a, yielded a p-value of
0.0750.075.
Interpret this result.
▼
Reject
Do not reject
the null hypothesis that the population coefficient of determination is
▼
less than
equal to
greater than
not equal to
enter your response here.
There
▼
is
is not
sufficient evidence to claim that average payoff and punishment use are
nothingcorrelatedcorrelated.
(Type an integer or a decimal. Do not round.)
Part 3
c. Does the result, part b, imply that increasing punishment
directlydirectly
affectsaffects
thethe
player'splayer's
payoffpayoff?
A.
Nolong dash—a
causal relationship cannot be inferred on the basis of high sample correlation.
B.
Yeslong dash—a
causal relationship may be inferred on the basis of the low p-value.
C.
The inference depends on the result of the corresponding regression analysis.
D.
The inference depends on the magnitude of the sample correlation coefficient. If its absolute value is greater than 0.9, then a causal relationship can be inferred.