Statistics Solutions

[Steps Shown] Let μ denote the mean value of some population. Suppose that in order to test \mathrmH_0: μ ≤q 1.5 against the alternative hypothesis

Question: Let \(\mu\) denote the mean value of some population. Suppose that in order to test

\[\mathrm{H}_{0}: \mu \leq 1.5\]

against the alternative hypothesis

\[\mathrm{H}_{1}: \mu>1.5\]

a sample is chosen from the population.

  1. Suppose for this sample that \(\mathrm{H}_{0}\) was not rejected. Does this imply that the sample data would have resulted in rejection of the null hypothesis if we had been testing the following?
    \[\mathrm{H}_{0}: \mu>1.5 \text { against } \mathrm{H}_{1}: \mu \leq 1.5\]
  2. Suppose this sample resulted in the rejection of \(\mathrm{H}_{0}\). Does this imply that the same sample data would have resulted in not rejecting the null

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