Question

In: Math

1. A researcher wants to know if being monolingual, bilingual, or multilingual is related to which...

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
  1. What kind of statistical test will you be performing?
  2. Will you need to test for equal variance? If so, what are your results and how does that influence the next steps in your analysis?
  3. What are your null and alternative hypotheses?
  4. Discuss the results of your analysis. Will you accept or reject your null hypothesis? Why? What can you specifically say about the data?

Solutions

Expert Solution

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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

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