## Answers

13)

The following cross tablulation have been provided. The row and column total have been calculated and they are shown below Column1 27 21 48 Column 2 20 34 54 Column 3 Row 1 Row 2 Total Total 60 60 120 13 18 The expected values are computed in terms of row and column totals. In fact, the formula is Ei C, where Ri corresponds to the total sum of elements in row i, C, corresponds to the total sum of elements in column j, and T is the grand total. The table below shows the calculations to obtain the table with expected values Expected Values Row 1 Row 2 Total Column1 48x604 48, 60-24 48 Column 2 54x6027 54x6027 54 Column 3 Total 60 60 120 18x60 120 120 120 18x60 120 120 120 18 Based on the observed and expected values, the squared distances can be computed according to the following formula: (E - O)2/E.

The table with squared distances is shown below Squared Distances Column1 (27-240.375 (21-242 0.375 Column 2 (20-27 1.815 34 27 1.815 Column 3 13-92 1.778 (5921.778 Row 1 24 9 Row 2 24 9

The following null and alternative hypotheses need to be tested: HO: The two variables are independent Ha: The two variables are dependent This corresponds to a Chi-Square test of independence. Based on the information provided, the significance level is a 0.05, the number of degrees of freedom is df (2 -1) x (3-1) 2, so then the rejection region for this test is R x2:X2 > 5.991 The Chi-Squared statistic is computed as follows: 0.375 +0.375 +1.815+1.8151.778+1.778-7.935 Since it is observed thatx2 -7.9352-5.991, it is then concluded that the null hypothesis is It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level.

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