Question

A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed. The sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypotheses using the rejection region method at a significance level of 0.05.

Answer #1

H0: 360 (Since 6 min = 6 * 60 = 360 seconds)

Ha: > 360

Test Statistic :-

t = ( X̅ - µ ) / (S / √(n) )

t = ( 370.69 - 360 ) / ( 24.36 / √(26) )

t = 2.2376

Test Criteria :-

Reject null hypothesis if t > t(α, n-1)

Critical value t(α, n-1) = t(0.05 , 26-1) = 1.708

t > t(α, n-1) = 2.2376 > 1.708

Result :- Reject null hypothesis

We conclude that we have sufficient evidence to support the claim that the data contradict prior belief.

A simulated exercise gave n = 24 observations on escape
time (sec) for oil workers, from which the sample mean and sample
standard deviation are 367.02 and 24.04, respectively. Suppose the
investigators had believed a priori that true average escape time
would be at most 6 min. Does the data contradict this prior belief?
Assuming normality, test the appropriate hypotheses using a
significance level of .05. (Give t to 2 decimal places and
the p-value to 3 decimal places.)

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
364
376
424
326
395
403
373
374
371
365
366
365
325
339
394
393
369
375
359
357
403
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...

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