In: Statistics and Probability
For reasons known only to social scientists, the General Social Survey (GSS) regularly asks its subjects their astrological sign. Here are the counts of responses for the 2012 GSS:
sign | Aries | Taurus | Gemini | Cancer | Leo | Virgo |
count | 145 | 167 | 170 | 158 | 185 | 158 |
sign | Libra | Scorpio | Sagittarius | Capricorn | Aquarius | Pisces |
count | 187 | 139 | 146 | 147 | 161 | 164 |
If births are spread uniformly across the year, we expect all 12 signs to be equally likely. Are they? Use α=0.05. χ2(±0.0001)= ________
P(±0.0001)=__________
a) There is evidence that all 12 signs are not equally likely.
b) There is no evidence that all 12 signs are not equally likely
The total number of persons is: 1927
If all the signs are equally likely then expected count in each category is
E = 1927 / 12 = 160.5833
Test statistic is
O: Observed frequency
E: Expected frequency.
O | E | (O-E) | (O-E)^2 | (O-E)^2/E | |
145 | 160.5833 | -15.5833 | 242.8403 | 1.512238 | |
167 | 160.5833 | 6.416667 | 41.17361 | 0.2564 | |
170 | 160.5833 | 9.416667 | 88.67361 | 0.552197 | |
158 | 160.5833 | -2.58333 | 6.673611 | 0.041559 | |
185 | 160.5833 | 24.41667 | 596.1736 | 3.71255 | |
158 | 160.5833 | -2.58333 | 6.673611 | 0.041559 | |
187 | 160.5833 | 26.41667 | 697.8403 | 4.345658 | |
139 | 160.5833 | -21.5833 | 465.8403 | 2.900925 | |
146 | 160.5833 | -14.5833 | 212.6736 | 1.324382 | |
147 | 160.5833 | -13.5833 | 184.5069 | 1.148979 | |
161 | 160.5833 | 0.416667 | 0.173611 | 0.001081 | |
164 | 160.5833 | 3.416667 | 11.67361 | 0.072695 | |
Total | 1927 | 15.91 |
Degrees of freedom = Number of E's - 1 = 12 - 1 = 11
The p-value of the test: 0.1445
Since the p-value is greater than α=0.05 so we fail to reject the null hypothesis.
There is no evidence that all 12 signs are not equally likely.