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.

389 357 359 363 375 424 325 394 402 373 374 371 364 366 364 326 339 393 393 369 375 359 356 404 335 397
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 371.15 and 24.36, 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%.

Answer 1

The upper confidence bound is approximately 380.74 seconds.

Step-by-step explanation:

To calculate an upper confidence bound for the population mean escape time, we can use the formula:

Upper bound = sample mean + (critical value * (sample standard deviation / sqrt(sample size)))

Given that the confidence level is 95%, the critical value for a sample size of 26 can be found using a t-distribution table or calculator.

Let's assume the critical value is 2.056.

Plugging in the values:

Upper bound = 371.15 + (2.056 * (24.36 / sqrt(26)))

Calculating the upper bound:

Upper bound = 371.15 + (2.056 * (24.36 / 5.099))

≈ 380.74

Therefore, the upper confidence bound for the population mean escape time is approximately 380.74 seconds.