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. 389 356 359 363 375 425 325 394 403 373 374 371 364 366 364 325 339 394 393 369 375 359 356 404 334 398 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 371.04 and 24.68, 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%. (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)? The upper prediction bound is lower than the upper confidence bound. The upper prediction bound is higher than the upper confidence bound. The upper prediction bound is equal to the the upper confidence bound. Correct: Your answer is correct. (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. ,

Answer 1

3 ANSWER & 24.68 126 The given data is. sample size n = 26 Sample mean T = 87801.24 371.04 Sample standard deviation 5 = 24.68 a.) The given upper confidence bound for the mean escape tome is ñ I tal-1) * I h 371.04 +1.708141 X 371.04 I 1.708141 X 4840164 371.04 £ 8.26 768383 (379.3076838, 362.7723162) b. The given 95% upper prediction bound for escape time of a single additional worker is * Ita, (n-D xs/itth 371.04 + 1.708141 * 24.68 x Vitez 371.04 + 1.708141 X 25,15013 371.04 I 42.95996 (413.99996, 328.08004) - Thanking you -