Question

Consider the following contingency table of observed frequencies. 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 the null and alternative hypotheses for a​ chi-square test of independence based on the information in the table. This test will have a significance level of

alphaαequals=0.100.10.

Choose the correct answer below.

A.

Upper H 0H0​:

The row and column variables are not independent of one another.

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 one another.

b. Calculate the expected frequencies for each cell in the contingency 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 squaredχ2equals=nothing

​(Round to the two decimal places as​ needed.)d. Using

alphaαequals=0.100.10​,

determine the​ chi-square critical value

chi Subscript alpha Superscript 2χ2α

and state your conclusions.

chi Subscript alpha Superscript 2χ2αequals=nothing

​(Round to two decimal places as​ needed.)

State your conclusions.

The test statistic

chi squaredχ2

is

▼

less than

greater than

the critical value

chi Subscript alpha Superscript 2χ2α​,

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 are independent.

the row and column variables are not independent of one another.the row and column variables are not independent of one another.

the row and column variables are independent of one another.the row and column variables are independent of one another.

at least one of the variables is not independent.at least one of the variables is not independent.

the variables Upper R 1 comma Upper R 1 comma Upper C 1 comma Upper 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 its meaning.

​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 the assumption that the

▼

alternative hypothesis

null hypothesis

is true. A​ p-value less than the significance level

alphaα

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

alphaαequals=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 one another.the row and column variables are not independent of one another.

none of the variables are independent.none of the variables are independent.

at least one of the variables is not independent.at least one of the variables is not independent.

the row and column variables are independent of one another.the row and column variables are independent of one another.

the variables Upper R 1 comma Upper R 1 comma Upper C 1 comma Upper 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).

Answer 1