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(See Solution) Consider the following set of samples obtained from fro normally distributed populations whose variances are equal: Sample 1 Sample 2 11.2

Question: Consider the following set of samples obtained from fro normally distributed populations whose variances are equal:

Sample 1 Sample 2
11.2 11.7
11.2 9.5
7.4 15.6
8.7 16.5
8.5 11.3
13.5 17.6
4.5 17
11.9 8.5
  1. Suppose that the samples were independent. Perform a test of hypothesis to determine if there is a difference in the two population means. Use a significance level of $0.05 .$
  2. Now suppose that the samples were paired samples. Perform a test of hypothesis to determine if there is a difference in the two population means.
  3. How do you account for the difference in the outcomes of part a and part b? Support your assertions with a statistical rationale.

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