An automobile mileage study tested the following hypotheses. Hypothesis Conclusion \[ H_{0}: \mu \geq 25 \mathrm{mpg} \] Manufacturer's claim supported \[ H_{\mathrm{a}}: \mu<25 \mathrm{mpg} \] Manufacturer's claim rejected; average mileage per gallon less than stated For $\sigma=3$ and a .02 level of significance, what sample size would be recommended if the researcher wants an $80 \%$ chance of detecting that $\mu$ is less than 25 miles per gallon when it is actually $24 ?$
Added by Robert A.
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We know that the power of a test is 1 - β, where β is the probability of making a Type II error (failing to reject the null hypothesis when it is false). In this case, we want the power of the test to be 0.80, so β = 0.20. We also know that the z-score Show more…
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An automobile mileage study tested the following hypotheses. Hypothesis: H0: μ ≥ 25 mpg Ha: μ < 25 mpg Conclusion: Manufacturer's claim supported Manufacturer's claim rejected; average mileage per gallon less than stated For σ = 3 and a .02 level of significance, what sample size would be recommended if the researcher wants an 80% chance of detecting that μ is less than 25 miles per gallon when it is actually 24? [Hint: Problem gave μa = 24 and (1-β) = 0.8.]
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