Perform a chi-square independence test using the critical value approach, provid

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 researcher performed a study to determine whether an association exists between sex and blood type. He obtained the following sample data.

at a 5% significance level do the data provide sufficient evidence to conclude that an association exists between sex and blood type?

PLease explain!

o a b ab total male 157 143 40 20 360 female 143 127 35 15 320 total 300 270 75 35 680

Explanation / Answer

To test the null hypothesis:

H0: Sex is independent of blood type.

against

H1: Sex is associated with blood type.

Under the null hypothesis , the expected frequencies are calculated using

Eij = (Ri)(Cj)/N where Ri = `ith row total and Cj = jth column total

Cal. Chi-square = sum(Oij2/Eij) - N

                          = 680.296 - 680 = 0.296

Tab. vale Chi-square at (2-1) and (4-1) i.e 3 d.f at 5% los =5.991

Since, Cal Chi- square < Tab. value of Chi- square so we do not reject the null hypothesis and conclude that there is no association between sex and blood type

Eij Oij Oij2/ Eij E11 = 158.824 157 155.197 E12 = 142.941 143 143.06 E13 = 39.706 40 40.296 E14 = 18.529 20 21.588 E21 = 141.177 143 144.847 E22 = 127.059 127 126.94 E23 = 35.294 35 34.708 E24 = 16.471 15 13.66

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