Perform a chi-square independence test using the critical value approach, provid
ID: 3159873 • Letter: P
Question
Perform a chi-square independence test using the critical value approach, provided the conditions for using the test are met. Be sure to state the hypotheses and the significance level, to obtain the expected frequencies, to obtain the critical value, to compute the value of the test statistic, and to state your conclusion.
A reasearcher performed a study to determine wheather an asssociation exists bewtween sex and blood type. He obtained the follwoing sample data.
Blood Type
Female
At the 5% significance level, do the data provide sufficent evidence to conclude that an association exists between sex and blood type?
O A B AB TotalFemale
157 143 40 20 360 Male 143 127 35 15 320 Total 300 270 75 35 680Explanation / Answer
Here,
Ho: Sex and blood type are independent.
Ho: Sex and blood type are not independent.
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We do this at 0.05 significance level.
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Doing an Expected Value Chart,
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 0.297187684 [TEST STATISTIC]
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With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 4
b = 2
df = 3 [DEGREES OF FREEDOM]
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Thus, the critical value is
significance level = 0.05
By table/technology,
chi^2(critical) = 7.814727903 [CRITICAL VALUE]
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As chi^2 < 7.815, we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that there is an association between sex and blood type at 0.05 level. [CONCLUSION]
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