A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will change when they are allowed to wear ear buds at work. A random sample of 8 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed.
Perform a Matched-Pairs hypothesis test for the claim that the time to complete the task has changed at a significance level of $\displaystyle \alpha={0.10}$.
If you wish to copy this data to a spreadsheet or StatCrunch, you may find it useful to first copy it to Notepad, in order to remove any formatting.
Round answers to 4 decimal places.

For the context of this problem, $\displaystyle \mu_{{d}}=\mu_{{{A}{f}{t}{e}{r}}}$ - $\displaystyle \mu$_Before,
where the first data set represents "after" and the second data set represents "before".
      $\displaystyle {H}_{{o}}:\mu_{{d}}={0}$
      $\displaystyle {H}_{{a}}:\mu_{{d}}\ne{0}$

This is the sample data:

After	Before
52.7	49.2
39.7	48.5
48.2	42.8
43.5	40.7
38.4	51.4
57.2	59.6
68.3	71.7
52.8	51

What is the mean difference for this sample?  
Mean difference =

What is the significance level for this sample?  
Significance level =

What is the P-value for this test?  
P-value =

This P-value leads to a decision to... Select an answer accept the null reject the claim fail to reject the null reject the null

As such, the final conclusion is that... Select an answer There is sufficient evidence to support the claim that the time to complete the task has changed. There is not sufficient evidence to support the claim that the time to complete the task has changed