
To test: the null hypothesis and show that it is rejected at the

Explanation of Solution
Given information :
Department | A | B | C | D | E | F | Total |
Male | 825 | 560 | 325 | 417 | 191 | 373 | 2691 |
Female | 108 | 25 | 593 | 375 | 393 | 341 | 1835 |
Total | 933 | 585 | 918 | 792 | 584 | 714 | 4526 |
Concept Involved:
In order to decide whether the presumed hypothesis for data sample stands accurate for the entire population or not we use the hypothesis testing.
The value of test statistics and the critical value identified from the table help us to decide whether to reject or do not reject null hypothesis.
The critical value from Table A.4, using degrees of freedom of
If
The values of two qualitative variables are connected and denoted in a contingency table.
This table consists of rows and column. The variables in each row and each column of the table represent a category.
The number of rows of contingency table is represented by letter ‘r’ and number of column of contingency table is represented by letter ‘c’.
The formula to find the number of degree of freedom of contingency table is
Calculation:
Finding the expected frequency for the cell corresponding to: | The expected frequency |
Number of male applicantsin department A The row total is 2691, the column total is 933, and the grand total is 4526. | |
Number of male applicantsin department B The row total is 2691, the column total is 585, and the grand total is 4526. | |
Number of male applicantsin department C The row total is 2691, the column total is 918, and the grand total is 4526. | |
Number of male applicantsin department D The row total is 2691, the column total is 792, and the grand total is 4526. | |
Number of male applicantsin department E The row total is 2691, the column total is 584, and the grand total is 4526. | |
Number of male applicantsin department F The row total is 2691, the column total is 714, and the grand total is 4526. | |
Number of female applicantsin department A The row total is 1835, the column total is 933, and the grand total is 4526. | |
Number of female applicantsin department B The row total is 1835, the column total is 585, and the grand total is 4526. | |
Number of female applicantsin department C The row total is 1835, the column total is 918, and the grand total is 4526. | |
Number of female applicantsin department D The row total is 1835, the column total is 792, and the grand total is 4526. | |
Number of female applicantsin department E The row total is 1835, the column total is 584, and the grand total is 4526. | |
Number of female applicantsin department F The row total is 1835, the column total is 714, and the grand total is 4526. |
All the expected frequencies are at least 5. From the results of previous part we have the below table:
Finding the value of the chi-square corresponding to: | |
Number of male applicantsin department A The observed frequency is 825 and expected frequency is 554.73 | |
Number of male applicantsin department B The observed frequency is 560 and expected frequency is 347.82 | |
Number of male applicantsin department C The observed frequency is 325 and expected frequency is 545.81 | |
Number of male applicantsin department D The observed frequency is 417 and expected frequency is 470.90 | |
Number of male applicantsin department E The observed frequency is 191 and expected frequency is 347.23 | |
Number of male applicantsin department F The observed frequency is 373 and expected frequency is 424.52 | |
Number of female applicantsin department A The observed frequency is 108 and expected frequency is 378.27 | |
Number of female applicantsin department B The observed frequency is 25 and expected frequency is 237.18 | |
Number of female applicantsin department C The observed frequency is 593 and expected frequency is 372.19 | |
Number of female applicantsin department D The observed frequency is 375 and expected frequency is 321.10 | |
Number of female applicantsin department E The observed frequency is 393 and expected frequency is 236.77 | |
Number of female applicantsin department F The observed frequency is 341 and expected frequency is 289.48 |
To compute the test statistics, we use the observed frequencies and expected frequency:
Here r represents the number of rows and c represents the number of columns.
Given
Degrees of freedom | Table A.4 Critical Values for the chi-square Distribution | |||||||||
0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 | 0.05 | 0.025 | 0.01 | 0.005 | |
1 | 0.000 | 0.000 | 0.001 | 0.004 | 0.016 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 |
2 | 0.010 | 0.020 | 0.051 | 0.103 | 0.211 | 4.605 | 5.991 | 7.378 | 9.210 | 10.597 |
3 | 0.072 | 0.115 | 0.216 | 0.352 | 0.584 | 6.251 | 7.815 | 9.348 | 11.345 | 12.838 |
4 | 0.207 | 0.297 | 0.484 | 0.711 | 1.064 | 7.779 | 9.488 | 11.143 | 13.277 | 14.860 |
5 | 0.412 | 0.554 | 0.831 | 1.145 | 1.610 | 9.236 | 11.070 | 12.833 | 15.086 | 16.750 |
Conclusion:
Test statistic: 1068.37; Critical value: 15.086.
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Chapter 12 Solutions
Elementary Statistics 2nd Edition
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