Question: Find the power. In Example 14.7 (page 351), a company medical director failed to find significant evidence that the mean blood pressure of a population of executives differed from the national mean \(\mu \) = 128. The medical director now wonders if the test used would detect an important difference if one were present. For the SRS of size 72 from a population with standard deviation \(\sigma \) = 15, the z statistic is

The two-sided test rejects \({{H}_{0}}:\mu =128\), at the 5% level of significance when \(|Z|\ge 1.96\)

1. Find the power of the test against the alternative \(\mu \) = 134.
2. Find the power of the test against \(\mu \) = 122. Can the test be relied on to detect a mean that differs from 128 by 6?
3. If the alternative were farther from H ₀ , say \(\mu \) = 136, would the power be higher or lower than the values calculated in (a) and (b)?

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