A contingency table containing observed values has four rows and five columns. The value of the chi-square statistic for testing independence is 22.87. Is
To find : whether
Answer to Problem 1CQ
Yes. The null hypothesis
Explanation of Solution
Given information : The value of chi-square statistics for testing independence is 22.87. A contingency table containing observed values has four rows and five columns.
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 contingency table of any given study is provided.
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:
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 |
6 | 0.676 | 0.872 | 1.237 | 1.635 | 2.204 | 10.645 | 12.592 | 14.449 | 16.812 | 18.548 |
7 | 0.989 | 1.239 | 1.690 | 2.167 | 2.833 | 12.017 | 14.067 | 16.013 | 18.475 | 20.278 |
8 | 1.344 | 1.646 | 2.180 | 2.733 | 3.490 | 13.362 | 15.507 | 17.535 | 20.090 | 21.955 |
9 | 1.735 | 2.088 | 2.700 | 3.325 | 4.168 | 14.684 | 16.919 | 19.023 | 21.666 | 23.589 |
10 | 2.156 | 2.558 | 3.247 | 3.940 | 4.865 | 15.987 | 18.307 | 20.483 | 23.209 | 25.188 |
11 | 2.603 | 3.053 | 3.816 | 4.575 | 5.578 | 17.275 | 19.675 | 21.920 | 24.725 | 26.757 |
12 | 3.074 | 3.571 | 4.404 | 5.226 | 6.304 | 18.549 | 21.026 | 23.337 | 26.217 | 28.300 |
13 | 3.565 | 4.107 | 5.009 | 5.892 | 7.042 | 19.812 | 22.362 | 24.736 | 27.688 | 29.819 |
14 | 4.075 | 4.660 | 5.629 | 6.571 | 7.790 | 21.064 | 23.685 | 26.119 | 29.141 | 31.319 |
15 | 4.601 | 5.229 | 6.262 | 7.261 | 8.547 | 22.307 | 24.996 | 27.488 | 30.578 | 32.801 |
Here degree of freedom is 12. The test statistics
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Chapter 12 Solutions
ELEMENTARY STATISTICS-ALEKS ACCESS 18W
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