Question

The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the

alpha equals 0.05α=0.05

level of significance.

	Category 1Category 1	Category 2Category 2	Category 3Category 3
FailuresFailures	6565	4040	4747
SuccessesSuccesses	5151	4040	5858

LOADING...

Click the icon to view the​ Chi-Square table of critical values.

State the hypotheses. Choose the correct answer below.

A.

Upper H 0H0​:

The

categories of the variablecategories of the variable

and

success and failuresuccess and failure

are independent.

Upper H 1H1​:

The

categories of the variablecategories of the variable

and

success and failuresuccess and failure

are dependent.

B.

Upper H 0H0​:

p11equals=p22equals=p33

Upper H 1H1​:

At least one of the proportions is different from the others.

C.

Upper H 0H0​:

The

categories of the variablecategories of the variable

and

success and failuresuccess and failure

are dependent.

Upper H 1H1​:

The

categories of the variablecategories of the variable

and

success and failuresuccess and failure

are independent.

D.

Upper H 0H0​:

muμ11equals=E11

and

muμ22equals=E22

and

muμ33equals=E33

Upper H 1H1​:

At least one mean is different from what is expected.

Compute the value of the​ chi-square test statistic.

chi Subscript 0 Superscript 2χ20equals=nothing

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

What range of​ P-values does the test statistic correspond​ to?

The​ P-value is

▼

between .01 and .025.

between .025 and .05.

greater than .10.

between .05 and .10.

less than .01.

What conclusion can be​ made?

A.The​ P-value is

greater than or equal togreater than or equal to

alphaα​,

so

do not rejectdo not reject

Upper H 0H0.

There is

not sufficientnot sufficient

evidence that the proportions are different from each other.

B.The​ P-value is

less thanless than

alphaα​,

so

do not rejectdo not reject

Upper H 0H0.

There is

sufficientsufficient

evidence that the proportions are different from each other.

C.The​ P-value is

less thanless than

alphaα​,

so

rejectreject

Upper H 0H0.

There is

not sufficientnot sufficient

evidence that the

categories of the variablecategories of the variable

and

success and failuresuccess and failure

are dependent.

D.The​ P-value is

greater than or equal togreater than or equal to

alphaα​,

so

rejectreject

Upper H 0H0.

There is

sufficientsufficient

evidence that the

categories of the variablecategories of the variable

and

success and failuresuccess and failure

are dependent.

Answer 1