Using the accompanying data below, perform a chi-square test using
alphaαequals=0.01
to determine if the proportion of "Yes" observations differs between Populations A and B.
Observed frequencies:
|
Population |
Yes |
No |
|
|---|---|---|---|
|
A |
18 |
20 |
|
|
B |
22 |
20 |
Expected frequencies:
|
Population |
Yes |
No |
|
|---|---|---|---|
|
A |
19 |
19 |
|
|
B |
21 |
21 |
Click the icon to view an excerpt from the table of chi-square critical values.
What are the null and alternative hypotheses?
A.
Upper H 0H0:
p Subscript Upper A Baseline not equals p Subscript Upper BpA≠pB
Upper H 1H1:
p Subscript Upper A Baseline equals p Subscript Upper BpA=pB
B.
Upper H 0H0:
p Subscript Upper A Baseline equals p Subscript Upper BpA=pB
Upper H 1H1:
p Subscript Upper A Baseline not equals p Subscript Upper BpA≠pB
C.
Upper H 0H0:
p Subscript Upper A Baseline equals p Subscript Upper BpA=pB
Upper H 1H1:
p Subscript Upper A Baseline greater than p Subscript Upper BpA>pB
D.
Upper H 0H0:
p Subscript Upper A Baseline equals p Subscript Upper BpA=pB
Upper H 1H1:
p Subscript Upper A Baseline less than p Subscript Upper BpA<pB
What is the test statistic?
chi squaredχ2equals=nothing
(Round to two decimal places as needed.)
What is the critical value?
chi Subscript alpha Superscript 2χ2αequals=nothing
(Round to three decimal places as needed.)
What is the correct conclusion?
A.
RejectReject
Upper H 0H0.
There
isis
enough evidence to conclude that the population proportions are different.
B.
RejectReject
Upper H 0H0.
There
is notis not
enough evidence to conclude that the population proportions are different.
C.
Do not rejectDo not reject
Upper H 0H0.
There
isis
enough evidence to conclude that the population proportions are different.
D.
Do not rejectDo not reject
Upper H 0H0.
There
is notis not
enough evidence to conclude that the population proportions are different.
Click to select your answer(s).
1) for hypothesis: option B is correct
2)
| Applying chi square test of independence: |
| chi square χ2 | =(Oi-Ei)2/Ei | pop 1 | pop 4 | Total |
| row 1 | 0.053 | 0.053 | 0.1053 | |
| row 2 | 0.048 | 0.0476 | 0.0952 | |
| total | 0.1003 | 0.1003 | 0.201 | |
| test statistic X2 = | 0.201 | |||
critical value χ2α = 6.635
option D is correct: do not reject Ho. there is not sufficient evidence.....
Using the accompanying data below, perform a chi-square test using alphaαequals=0.01 to determine if the proportion...
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