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Statistics- Hypothesis test, Two-tail and one-tail tests

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Question (1):
A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means?

Question (2):
Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information(Please refer the table in attached question file).
At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value?

Question (3):
The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random and their weekly incomes before and after the plan were recorded(Please refer the table in attached question file)
Was there a significant increase in the typical salesperson's weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it.
( For complete description of questions, please see the attached questions file.

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Solutions to the posted problems are given with step by step explanation in such a way that the student can easily understand the concept and use the same solutions as model solutions to solve other type of similar problems.
Formulas, procedure, working and simplifications with arriving at the final result and interpretation of results are given in a clear and concise manner so as to avoid any kind of confusion in using these solutions for solving other problems on one-tail and two-tail hypothesis test problems in statistics.

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Solution (1):

Sample Mean : Population I = 350 , Population II = 342
Sample Standard Deviation : Population I = 12 , Population II = 15
An unbiased estimate of the common population standard deviation = 13.68
Standard Error of the difference between two means = 4.8455
Value of t = 1.6510

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