A sample of 26 offshore oil workers took part in a simulated escape exercise, re

Question

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. 389 357 359 363 376 425 326 395 403 374 374 371 365 366 365 326 339 394 392 369 375 359 356 403 334 397 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 371.23 and 24.40, respectively. (Round your answers to two decimal places.) (a) Calculate an upper confidence bound for population mean escape time using a confidence level of 95%. 379.40 (b) Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%. 413.70 How does this bound compare with the confidence bound of part (a)? The upper prediction bound is higher than the upper confidence bound. The upper prediction bound is lower than the upper confidence bound. The upper prediction bound is equal to the the upper confidence bound. (c) Suppose tht two additional workers will be chosen to participate in the simulated escape exercise. Denote their escape times by X27 and X2s, 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. 333.88 X407.50

Explanation / Answer

Solution:-

c) X +/- t(0.05,25) * s * sqrt((1/n)+(1/2))

= 371.23 +/- 2.060 * 24.40 * sqrt((1/26)+(1/2))
  
= (334.35 , 408.11)

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