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

The degrees of freedom are given by:

And the p value would be:

If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change

Step-by-step explanation:

Information given

represent the sample mean

represent the sample standard deviation

sample size  

represent the value to verify

z would represent the statistic

represent the p value

Hypothesis to test

We want to check if the true mean is at most 360 seconds, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic for this case would be given by:

(1)  

We can replace in formula (1) the info given like this:  

The degrees of freedom are given by:

And the p value would be:

If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8