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Large sample tests for Means and proportions based on single and two samples using R

1. Given below are the gain in weights of calves on two different diets A and B. Test whether there is any significant difference in the mean weight of calves of 2 diets. A 30,28,27,22,50,71,9,68,10,83,78,41,67,72,67,22,94,19,43,28,72,41,6,16,77,93,15,54,89,47,24 B 20,5,35,43,13,13,60,43,78,88,60,23,31,94,26,59,70,52,5,20,19,3,82,59,9,44,30,90,80,29

2. In a random sample of 400 persons from a large population, 120 are females. Can it be said that males and females are in the ratio 5:3 in the population? Use 1% level of significance.

3. The subject under investigation is the measure of dependence of Tamil on words of Sanskrit origin. One newspaper article reporting the proceedings of the constituent assembly contained 2025 words of which 729 words were declared by literacy critic to be of Sanskrit origin. A second article by the author describing atomic research contained 1600 words of which 640 words were declared by the same critic to be of Sanskrit origin. Examine whether there is any significant difference in the dependence of this writer or words of Sankrit origin in writing the two articles.