Question

You are a well-respected organizational consultant, and you have a small business client who is interested in better understanding how to analyze business data from samples. Your client wants to make sure the organization is operating efficiently and effectively. There is no one in the client’s business with statistical analysis expertise and who wants to learn from you. The client has provided you with data to compare the means of two independent populations. You have a sample of n1 = 8 with the sample mean ??1 = 42 and a sample standard deviation, S = 4, and you have an independent sample of n2 15 from another population with a sample mean of ??2=34 and a sample standard deviation of S2=5

H₀ : µ₁ = µ₂ or H₁ : µ₁ ≠ µ₂

Pooled Variance = 22

t-STAT test statistic = 3.8959

There are 21 degrees of freedom and the critical value for t is 2.0796

Upper critical value is 2.0796 and lower critical value -2.0796

The p-value is 0.0008

If t does not fall between 2.0796 and -2.0796, then reject the null hypothesis.

The t-STAT is 3.8959, so the null hypothesis should be rejected.

Normal distribution is the assumption.    

95% CI estimate is (3.729, 12.270)

Given your initial analysis of the data, do you believe a problem exists at the client facility that requires further examination? If so, what additional data would you need to analyze to understand the nature of the problem in order to make a recommendation for improvement? (200-250 words). Make certain you explain and interpret the entire process to the client because they are interested in learning about how two-sample tests can be used to make business decisions.

Answer 1