Consider the following contingency table that is based on a sample survey. a. Wr

Question

Consider the following contingency table that is based on a sample survey.

a. Write the null and alternative hypotheses for a test of independence for this table.

H0: Rows and columns are

H1: Row and columns are

b. Calculate the expected frequencies for all cells assuming that the null hypothesis is true.

Round your answers to three decimal places, where required.

c. For =0.01, find the critical value of 2. Specify the rejection and nonrejection regions on the chi-square distribution curve.

Enter the exact answer from the chi-square distribution table.

of the critical value of 2.
The nonrejection region is

of the critical value of 2.

d. Find the value of the test statistic 2.

Round your answer to three decimal places.

e. Using =0.01, would you reject the null hypothesis?

Column 1 Column 2 Column 3 Row 1 139 90 73 Row 2 90 51 92 Row 3 129 69 118

Explanation / Answer

aH0: Rows and columns are independent

b) Row and columns are dependent

b)

c) critical 2=13.2767

rejection regio is chi stat on the right of the critical value of 2

d)value of the test statistic 2 =18.677

e) Yes

Observed O column1 column2 column3 Total row1 139 90 73 302 row2 90 51 92 233 row3 129 69 118 316 Total 358 210 283 851 Expected E=rowtotal*column total/grand total column1 column2 column3 Total row1 127.046 74.524 100.430 302 row2 98.019 57.497 77.484 233 row3 132.935 77.979 105.086 316 Total 358 210 283 851 chi square =(O-E)^2/E column1 column2 column3 Total row1 1.125 3.2138 7.4919 11.830 row2 0.656 0.734 2.719 4.110 row3 0.117 1.034 1.587 2.737 Total 1.897 4.982 11.798 18.677

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