A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape: 383 351 354 362 379 422 321 395 401
374 376 371 362 366 366 325 339 393
393 368 377 358 353 409 330 398
A normal probability plot of the n = 26 observations on escape time given above shows a substantial linear pattern; the sample mean and sample standard deviation are 371.08 and 24.45, respectively.
(a) Calculate an upper confidence bound for population mean escape time using a confidence level of 95%.
(b) Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%. How does this bound compare with the confidence bound of part (a)?
(1) The upper prediction bound is equal to the the upper confidence bound.
(2) The upper prediction bound is lower than the upper confidence bound.
(3) The upper prediction bound is higher than the upper confidence bound.
(c) Suppose that two additional workers will be chosen to participate in the simulated escape exercise. Denote their escape times by X27 and X28, and let Xnew denote the average of these two values. Modify the formula for a PI for a single x value to obtain a PI for Xnew, and calculate a 95% two-sided interval based on the given escape data.