Question: PROBABILITY AT STATS: (PLEASE ANSWER IN FULL DETAIL AND EXPLANATIONS) ? Let the following numbers represent the order statistics of the n = 27 obser-

PROBABILITY AT STATS: (PLEASE ANSWER IN FULL DETAIL AND EXPLANATIONS)

Let the following numbers represent the order statistics of the n = 27 obser- vations 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 We are interested in estimating the 25th percentile, 7:025, of the population. Since (n + 1) p = 28(1/ 4) = 7, the seventh order statistic, namely, y7 = 283, would be a point estimate of 7:025. For interval estimate, we would like to use the interval (y4,y10) for esti- mating 7150,25. Compute the condence of this interval estimate. (Justify your reasoning.)

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