A simulated exercise gave n 24 observations on escape time

A simulated exercise gave n = 24 observations on escape time (sec) for oil workers, from which the sample mean and sample standard deviation are 367.7 and 24.55, 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.)

Solution

t = (x-bar - mu)/(s/sqrt(n))

Here, x-bar = 367.7

mu = 360

s = 24.55

n = 24

Therefore, t = (367.7 - 360)/(24.55/sqrt(24))

= 1.54

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The p-value corresponding to t = 1.54 and df = 23 is 0.069 {from calculator)