In: Math
1. A researcher wants to know if being monolingual, bilingual, or multilingual is related to which country a person is from. To assess this, a large group of people were surveyed. The results of that survey are reported below. Are the traits related?
obs freq | monolingual | bilingual | multilingual |
USA | 127 | 12 | 10 |
CANADA | 84 | 25 | 12 |
MEXICO | 134 | 9 | 8 |
ENGLAND | 133 | 23 | 19 |
SPAIN | 56 | 49 | 17 |
FRANCE | 108 | 25 | 15 |
GERMANY | 47 | 80 | 14 |
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a).
Since dependent variable is (nominal type) i.e. country and independent variables are of (interval/ratio) type. We will use chi-square test of independence based on the claim.
b).
Since, Chi-square statistic is a non-parametric (distribution free) statistic.Thus it does not require equality of variance among the study groups or homoscedasticity in the data just like all non parametric statistics.
c).
Null : Linguistic character of a person is independent of the country he belongs to.
Alternate : Linguistic character and country of a person is dependent.
alpha = 0.05- level of significance.
d).
Below is the hypothesis testing.
Contingency table | ||||||||
Row | Column | fo | Rt | Ct | fe | (fo - fe) | (fo - fe)^2 | (fo - fe)^2/fe |
1 | 1 | 127 | 149 | 689 | 101.947 | 25.053 | 627.634 | 6.156 |
1 | 2 | 12 | 149 | 223 | 32.996 | -20.996 | 440.833 | 13.360 |
1 | 3 | 10 | 149 | 95 | 14.057 | -4.057 | 16.456 | 1.171 |
2 | 1 | 84 | 121 | 689 | 82.789 | 1.211 | 1.465 | 0.018 |
2 | 2 | 25 | 121 | 223 | 26.795 | -1.795 | 3.224 | 0.120 |
2 | 3 | 12 | 121 | 95 | 11.415 | 0.585 | 0.342 | 0.030 |
3 | 1 | 134 | 151 | 689 | 103.316 | 30.684 | 941.521 | 9.113 |
3 | 2 | 9 | 151 | 223 | 33.439 | -24.439 | 597.261 | 17.861 |
3 | 3 | 8 | 151 | 95 | 14.245 | -6.245 | 39.004 | 2.738 |
4 | 1 | 133 | 175 | 689 | 119.737 | 13.263 | 175.911 | 1.469 |
4 | 2 | 23 | 175 | 223 | 38.754 | -15.754 | 248.180 | 6.404 |
4 | 3 | 19 | 175 | 95 | 16.509 | 2.491 | 6.203 | 0.376 |
5 | 1 | 56 | 122 | 689 | 83.474 | -27.474 | 754.803 | 9.042 |
5 | 2 | 49 | 122 | 223 | 27.017 | 21.983 | 483.257 | 17.887 |
5 | 3 | 17 | 122 | 95 | 11.509 | 5.491 | 30.146 | 2.619 |
6 | 1 | 108 | 148 | 689 | 101.263 | 6.737 | 45.385 | 0.448 |
6 | 2 | 25 | 148 | 223 | 32.775 | -7.775 | 60.444 | 1.844 |
6 | 3 | 15 | 148 | 95 | 13.962 | 1.038 | 1.077 | 0.077 |
7 | 1 | 47 | 141 | 689 | 96.474 | -49.474 | 2447.645 | 25.371 |
7 | 2 | 80 | 141 | 223 | 31.224 | 48.776 | 2379.056 | 76.192 |
7 | 3 | 14 | 141 | 95 | 13.302 | 0.698 | 0.487 | 0.037 |
192.335 |