Please show me the question of 4 and 5 Let the following numbers represent the order statistics y₁, 92,927 of the n = 27observations obtained in a random sample from a certain population of incomes (measuredin hundreds of dollars):261 269 271 274 279 280 283 284 286 287 292 293 296 300304 305 313 321 322 329 341 343 356 364 391 417 476(i) Let Fx be the cumulative distribution function (CDF) of this population. Give a 95%confidence interval for p = Fx (350) based on the given sample.(ii) Give a point estimate for the 80th percentile of this population, To.8, based on thegiven sample.(iii) Suppose we use (yi, yj) as an interval estimate for 70.8. Express the approximateconfidence level for this interval in the formP(70.8 € (Y₁, Yj)) ≈ P(N(0, 1) = [a, b])where a, b are expressions involving i, j. To achieve a given confidence level 1 - a, wemay set a = -a/2, b = a/2 in the equation above. Solve for i and j in terms of Za/2.(iv) Follow this procedure to give an approximate 95% confidence interval for 0.8 basedon the given sample. (Round i and j to nearest integer.)(v) Compute the exact confidence level of the interval you found in the previous part.(You probably want to use a computer for this.) Suppose a new drug is available for treating high blood pressure. We want to investigateits effect by running a controlled experiment:. We randomly select some patients with high blood pressure and randomly divide theminto two groups, Group A and Group B.1● We then give the actual drug to patients in Group A and a placebo (i.e. non-harmfulfake drug) to patients in Group B.Let X be the amount of blood pressure reduction in a patient taking the new drug, andY the amount of blood pressure reduction in a patient taking the placebo. Assume thatX Nux, 12) and Y~ N(μy, 8). How many patients (in total) do we need to selectfor participation in this experiment, if we want to construct a 95% confidence interval for"xy with length < 2?

iv) 95% confidence interval for π0.8 based on the given sample is, Arrange the data in ascending…

Let the following numbers represent the order statistics ₁, 2, ,927 of the n 27 observations obtained in a random sample from a certain population of incomes (measured in hundreds of dollars): = 261 269 271 274 279 280 283 284 286 287 292 293 296 300 304 305 313 321 322 329 341 343 356 364 391 417 476 (i) Let Fy be the cumulative distribution function (CDF) of this population. Give a 95%