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. 389 357 359 363 376 424 325 395 403 367 365 325 339 393 374 373 371 365 392 369 375 359 357 403 335 398 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 371.19 and 24.37, 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 higher than the upper confidence bound. The upper prediction bound is equal to the the upper confidence bound. The upper prediction bound is lower than the upper confidence bound. (c) denote the average of these two 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 X values. Modify the formula for a PI for a single x value to obtain a PI for X and calculate a 95% two-sided interval based on the given escape data. new new'

Answer 1

To calculate an upper confidence bound for the population mean escape time using a confidence level of 95%, the formula is used. To calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%, a different formula is used. The upper prediction bound is higher than the upper confidence bound.

Step-by-step explanation:

To calculate an upper confidence bound for the population mean escape time using a confidence level of 95%, we can use the formula:

Upper Confidence Bound = Sample Mean + Critical Value * (Sample Standard Deviation / sqrt(Sample Size))

Using the given data, the upper confidence bound is calculated as:

Upper Confidence Bound = 371.19 + 1.96 * (24.37 / sqrt(26)) = 394.62

To calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%, we can use the formula:

Upper Prediction Bound = Sample Mean + Critical Value * (Sample Standard Deviation)

Using the given data, the upper prediction bound is calculated as:

Upper Prediction Bound = 371.19 + 1.96 * 24.37 = 418.05

The upper prediction bound is higher than the upper confidence bound.

Answer 2

The calculation of confidence and prediction intervals using statistical techniques for a given set of data on escape times for offshore oil workers.

Step-by-step explanation:

The mean escape time for a sample of offshore oil workers and the calculation of confidence and prediction intervals based on the sample data. Confidence and prediction intervals are both methods to estimate population parameters, but they serve different purposes and are calculated differently.

For part (a), we calculate an upper confidence bound for the population mean escape time, for part (b), an upper prediction bound for the escape time of an additional worker, and for part (c), a two-sided prediction interval for the mean escape time of two additional workers.