Concept explainers
To find: Whether there is sufficient evidence to conclude that there is a significant different in the distribution of city by race at 5% significance level.
Answer to Problem 12E
Yes, there is a significant different in the distribution of city by race at 5% significance level.
Explanation of Solution
Given:
The proportion values are 0.28, 0.24, 0.35, 0.12 and 0.01.
The table is:
212 |
202 |
270 |
94 |
22 |
Formula used:
The formula to compute the test statistic is
Calculation:
The null and alternative hypotheses are:
The calculation for test statistic is done as:
Observed value | ||||
0.28 | 224 | -12 | 144 | 0.6429 |
0.24 | 192 | 10 | 100 | 0.5208 |
0.35 | 280 | -10 | 100 | 0.3571 |
0.12 | 96 | -2 | 4 | 0.0417 |
0.01 | 8 | 14 | 196 | 24.5 |
The test statistic is:
The degree of freedom is calculated as:
The p-value using chi-square table at 4 degree of freedom is 0.00003
The p -value is below significance level. The null hypothesis gets rejected. Thus, there is a significant different in the distribution of city by race at 5% significance level.
Chapter 11 Solutions
The Practice of Statistics for AP - 4th Edition
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