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. 389 374 393 356 359 363 374 370 365 369 374 359 375 366 357 425 325 365 326 404 335 395 403 339 393 398 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 24.50, 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) Suppose that two additional workers will be chosen to participate in the simulated escape exercise. Denote their escape times by X27 and X2g, and let denote the average of these two values. Modify the formula for a PI for a single x value to obtain a PI for new and calculate a 95% two-sided interval based on the given escape data. new

Answer 1

a)

sample mean 'x̄=		371.1900
sample size    n=		26
std deviation s=		24.5000
std error ='sx=s/√n=24.5/√26=		4.8048

for 95% upper CI; and 25 df, value of t=		1.7080		from excel: t.inv(0.95,25)
margin of error E=t*std error    =		8.2067

Upper bound=sample mean+E =

379.40

b)

std errror of mean ='sx=s*√(1+1/n)=		24.967
for 95% CI; and 25 df, value of t=		1.708		from excel: t.inv(0.95,25)
margin of error E=t*std error    =		42.6431

Upper bound=sample mean+E=

413.83

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

c)

std errror of mean ='sx=s*√(1/2+1/n)=		17.978
for 95% CI; and 25 df, value of t=		2.0600
margin of error E=t*std error    =		37.03
lower bound=sample mean-E =		334.16
Upper bound=sample mean+E=		408.22

95% CI =(334.16 , 408.22)