May you help me to answer Q5 - Q6 and Q7?

5. By enumeration of cases obtain the null distribution of D when (i) N = 3; (ii) N = 4. 6. Suppose that in Example 3. the measure of interest is not the total number of illegitimate births but the number of such births per 1,000 total live births. These ratios are as follows:1 1940 1945 1947 1950 1955 1957 Alabama 17.0 16.2 12.5 12.9 13.2 14.2 Delaware 29.3 25.1 23.5 24.0 18.6 18.2 District of Columbia 23.8 34.9 32.6 31.7 43.3 58.8 Kansas 11.5 18.3 13.2 12.6 13.9 14.5 Lousiana 17.4 14.7 17.7 12.4 13.3 13.1 (i) Test whether these ratios have tended to increase in time. (ii) Test whether the ratios tend to form a consistent pattern from state to state by applying F riedman's statistic Q with the states as blocks and the years as \"treatments.\" Discuss the appropriateness of the test statistic and its null distribution. 7. Given the following hypothetical IQ scores of a child at the indicated ages (in years), test the hypothesis of randomness against the alternative of an upward trend. Age 3 31 4 4i, 5 Si 6 7 8 9 10 11 I2 IQ 130 132 136 133 135 138 141 140 I37 139 150 153 160