The escape time (sec) for oil workers in a simulated exercise, gave the sample mean 370.69, sample standard deviation 24.36, and number of observations as n =26. 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 hypothesis using a significance level of .05.

Null hypothesis:      

Alternative hypothesis:      

The statistic is given by:

(1)      

Replacing the info we got:

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes

Step-by-step explanation:

Information given

represent the sample mean

represent the standard deviation for the sample    

sample size      

represent the value to verify

represent the significance level

t would represent the statistic

represent the p value

System of hypothesis

We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:      

Null hypothesis:      

Alternative hypothesis:      

The statistic is given by:

(1)      

Replacing the info we got:

The degrees of freedom are:

The p value would be given by:

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal