You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.
X | Y | Z | |
---|---|---|---|
A | 26 | 26 | 47 |
B | 30 | 26 | 17 |
Give all answers rounded to 3 places after the decimal point, if necessary.
(a) Enter the expected frequencies below:
X | Y | Z | |
---|---|---|---|
A | |||
B |
(b) What is the chi-square test-statistic for
this data?
Test Statistic: χ2=χ2=
(c) What is the critical value for this test of
independence when using a significance level of αα = 0.025?
Critical Value:
χ2=χ2=
(d) What is the correct conclusion of this hypothesis test at the 0.025 significance level?
Remember to give all answers rounded to 3 places after the decimal point, if necessary.
Show steps on graphing calculator
Observed (O) | ||||
X | Y | Z | Total | |
A | 26 | 26 | 47 | 99 |
B | 30 | 26 | 17 | 73 |
Total | 56 | 52 | 64 | 172 |
a) The expected frequency are
Expected (E ) | |||
X | Y | Z | |
A | 32.23 | 29.93 | 36.84 |
B | 23.77 | 22.07 | 27.16 |
b)
(O-E)^2/E | |||
X | Y | Z | |
A | 1.21 | 0.52 | 2.80 |
B | 1.63 | 0.70 | 3.80 |
Observed (O) | ||||
X | Y | Z | Total | |
A | 26 | 26 | 47 | 99 |
B | 30 | 26 | 17 | 73 |
Total | 56 | 52 | 64 | 172 |
Expected (E ) | ||||
X | Y | Z | ||
A | 32.233 | 29.930 | 36.837 | |
B | 23.767 | 22.070 | 27.163 | |
(O-E)^2/E | ||||
X | Y | Z | ||
A | 1.205 | 0.516 | 2.804 | |
B | 1.634 | 0.700 | 3.802 |
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