(c) A random sample of 200 married clinical academic doctors, all retired, was classified according to seniority and number of children: Children: Seniority: 0-2 3-4 More than 4 Academic clinical...

Extracted text: (c) A random sample of 200 married clinical academic doctors, all retired, was classified according to seniority and number of children: Children: Seniority: 0-2 3-4 More than 4 Academic clinical fellow 32 25 16 Clinical lecturer 44 18 22 Clinical research fellow 22 8 13 Test the hypothesis (Ho: The size of family is independent of level of seniority) that the size of a family is independent of the level of seniority attained by the doctors at the 0.05 level of significance. Use the chi-squared critical value approach.


Extracted text: (а) The performances in a statistics course with 100 students for a particular semester were as follows: Grade A В F Number of students 18 25 32 20 5 At the 0.05 level of significance, test the hypothesis that the distribution of performance is uniform (Ho: The data is uniformly distributed). Use the chi-squared critical value approach. (b) Given the variance of a chi-squared distribution is 2v, where v is the degrees of freedom. Show that the variance of S for random samples of size n from a normal population decreases as n increases.