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Human Resource director of a large company wants to investigate if professional staff takes longer coffee breaks than their technical counterparts. She takes a random sample of 10 professionals and another sample of 10 technicians in the company and determines via their supervisors the amount of time (in minutes) they spent for the coffee breaks during a specific day. The results are available in the Assign2Data.xlsx file., answer the following questions.

Assign2Data:

Professionals	Technicians
23	23
18	21
34	24
31	23
28	28
33	25
25	21
27	21
32	26
21	17

(a) Assess whether the assumptions/conditions for performing a two-sample t-test to compare break time between the two groups of employees are warranted (justify your answers).

(b) Irrespective of your answer in (a) above, test at 5% level of significance whether the professional employees take longer coffee breaks than their technical counterparts. Assume the two population variances are the same and use both the critical value and p-value approaches (using approximate values from t distribution table). Show all the steps of your hypothesis test (hypotheses, significance level, test statistic, decision criteria, critical value, p-value, decision with justification). (Manual Calculations)