Consider the following contingency table of observedfrequencies. Complete parts a. through e. below.
Column Variable | |
|---|
Row Variable | Upper C 1C1 | Upper C 2C2 | Upper C 3C3 | |
|---|
Upper R 1R1 | 2020 | 77 | 1818 | |
Upper R 2R2 | 88 | 88 | 1313 | |
Upper R 3R3 | 88 | 1616 | 6 |
Click the icon to view the contingency table.a. Identify thenull and alternative hypotheses for a? chi-square test ofindependence based on the information in the table. This test willhave a significance level of
alpha?equals=0.100.10.
Choose the correct answer below.
A.
Upper H 0H0?:
The row and column variables are not independent of oneanother.
Upper H 1H1?:
The row and column variables are independent of one another.
B.
Upper H 0H0?:
The variables
Upper R 1R1?,
Upper R 2R2?,
Upper R 3R3?,
Upper C 1C1?,
Upper C 2C2?,
and
Upper C 3C3
are independent.
Upper H 1H1?:
At least one of the variables is not independent.
C.
Upper H 0H0?:
The variables
Upper R 1R1?,
Upper R 2R2?,
Upper R 3R3?,
Upper C 1C1?,
Upper C 2C2?,
and
Upper C 3C3
are independent.
Upper H 1H1?:
None of the variables are independent.
D.
Upper H 0H0?:
The row and column variables are independent of one another.
Upper H 1H1?:
The row and column variables are not independent of oneanother.
b. Calculate the expected frequencies for each cell in thecontingency table.
| | Column Variable |
|---|
Row Variable | Upper C 1C1 | Upper C 2C2 | Upper C 3C3 |
|---|
Upper R 1R1 | nothing | nothing | nothing |
Upper R 2R2 | nothing | nothing | nothing |
Upper R 3R3 | nothing | nothing | nothing |
?(Round to two decimal places as? needed.) |
c. Calculate the? chi-square test statistic.
chi squared?2equals=nothing
?(Round to the two decimal places as? needed.)d. Using
alpha?equals=0.100.10?,
determine the? chi-square critical value
chi Subscript alpha Superscript 2?2?
and state your conclusions.
chi Subscript alpha Superscript 2?2?equals=nothing
?(Round to two decimal places as? needed.)
State your conclusions.
The test statistic
chi squared?2
is
?
less than
greater than
the critical value
chi Subscript alpha Superscript 2?2??,
so
?
do not reject
reject
the
?
alternative hypothesis.
null hypothesis.
There is
?
insufficient
sufficient
evidence to indicate that
?
none of the variables are independent.none of the variables areindependent.
the row and column variables are not independent of oneanother.the row and column variables are not independent of oneanother.
the row and column variables are independent of one another.therow and column variables are independent of one another.
at least one of the variables is not independent.at least one ofthe variables is not independent.
the variables Upper R 1 comma Upper R 1 comma Upper C 1 commaUpper C 2 comma and Upper C 3 are independent.the variables R1, R1,C1, C2, and C3 are independent.
e. Determine the? p-value using technology and interpret itsmeaning.
?p-valueequals=nothing
?(Round to three decimal places as? needed.)
Interpret the meaning of the? p-value.
The? p-value is the probability of observing a
?
critical value
test statistic
as extreme or more extreme than the one observed under theassumption that the
?
alternative hypothesis
null hypothesis
is true. A? p-value less than the significance level
alpha?
means that the
?
critical value
test statistic
is
?
unlikely
likely
enough that the
?
alternative hypothesis
null hypothesis
should be rejected. For this? test, the? p-value is
?
less than
greater than
alpha?equals=0.100.10?,
so
?
do not reject
reject
the
?
alternative hypothesis.
null hypothesis.
There is
?
sufficient
insufficient
evidence to indicate that
?
the row and column variables are not independent of oneanother.the row and column variables are not independent of oneanother.
none of the variables are independent.none of the variables areindependent.
at least one of the variables is not independent.at least one ofthe variables is not independent.
the row and column variables are independent of one another.therow and column variables are independent of one another.
the variables Upper R 1 comma Upper R 1 comma Upper C 1 commaUpper C 2 comma and Upper C 3 are independent.the variables R1, R1,C1, C2, and C3 are independent.
Click to select your answer(s).
