p - value = The P-Value is .001481.
conclusion-
Option b) is correct.
Part - 2)
p- value = is < .00001
conclusion -
option b) is correct.
last question -
option d) is correct
The expected values are computed in terms of row and column totals. In fact, the formula is Ei where R 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 Row 3 Row 4 Total Column1 Column 2 Column 3 12x40.8 12 30-б Total 4 30 16 10 60 26 х 4 1.467 22x30 11 22165.867 22x103.667 601.733 00013 26x166.933 60 26x30 60 12x163.2 12x102 12 60 60 60 60 26x104.333 60 26 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 Column 2 0-1.4671.467 0.364 567 2.912 (3-3,6670.121 Column 3 0-0.8 0.8 Row 1 18-131.923 3-6 Row 2 4-3.2_0.2 2-6.933)2 Row 3 9333.51 (2-4.333 1.256 Row 4 th 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 Rejection Region Based on the information provided, the significance level is a 0.01,the number of degrees of freedom is df (4-1) x (3-1) 6, so then the rejection region for this test is R x2x216.812)
Test Statistics The Chi-Squared statistic is computed as follows: X2 0%-Gr 2.964-1.923 + 3.51 + 1.256 + 1.467 + 0.364 + 2.912 + 0.121 + 0.8 + 1.5 + 0.2 + 4.5-21.517 72 27 Decision about the null hypothesis Since it is observed that χ2-21.517 > x2 null hypothesis is rejected. 16.812, it is then concluded that the Conclusion t is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.01 significance level
Total 29 86 40 Expected Values Row 1 Row 2 Row 3 Row 4 Total Column1 43x27.745 43x86 22.969 43x 40 10.683 6.602 43 Column 2 55x29 9.907 55x86 29.379 Column 3 T 11.348 63x8633.652 63x4015.652 62.348 63 161 161 161 161 161 40 13,665 161 161 161 55x6 T016 2.05 161 161 161 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 Column 2 Column 3 21-7.745 901.541 2-11.3487.7 Row 1 22.683 (28-33.65220.949 39-29.3793.151 19-22.9690.686 Row 2 30-15.652) 1-13665 3.251 3-10.683 Row 3 15.652 13.152 10683 5.526 13.665- 0.1.602 (3TDs_ = 0.441 (3-2.348 0.181 0-1.602)2 Row 4 6021.602
Rejection Region Based on the information provided, the significance level is α 0.01 , the number of degrees of freedom is df - (4-1) x (3-1) 6, so then the rejection region for this test is R [x2 : x2 > 16.812 The Chi-Squared statistic is computed as follows 12 (Oij-Eij)" 22.683+0.686+5.526 +1.602+1.541 3.151+3.2510.441+7.7+0.949+13.152+0.181 21 Decision about the null hypothesis Since it is observed that χ2-60.862 > x2 null hypothesis is rejected Conclusion 16.812, it is then concluded that the 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 0.01 significance level.