Question

In a test of the hypothesis H0: p = 0.8 against Ha: p > 0.8, the power of the test when p = 0.9 is greatest for which of the following?

n = 75, α = 0.05
n = 75, α = 0.10
n = 70, α = 0.10
n = 70, α = 0.05
There is not enough information given to draw a conclusion.

Answer 1

`\Huge \boxed{\boxed{\bf{n = 75, \alpha = 0.10}}}`

Step-by-step explanation:

To determine which option has the greatest power, we need to consider the sample size (n) and the significance level (α). The probability of correctly rejecting the null hypothesis when it is false is the test's power. Higher power tests are more likely to detect a true effect.

The sample size and significance level also affect power. A higher power is typically achieved by using a larger sample size and a higher significance level (α). We can compare the options:

◙ Options 1 and 2 have the same sample size (n = 75), but option 2 has a higher significance level (α = 0.10), which should result in a higher power.

◙ Options 3 and 4 have the same sample size (n = 70), but option 3 has a higher significance level (α = 0.10), which should result in a higher power.

◙ Comparing options 2 and 3, option 2 has a larger sample size (n = 75) and the same significance level (α = 0.10), which should result in a higher power.

Therefore, the power of the test when p = 0.9 is greatest for the option with n = 75 and α = 0.10.

#BTH1

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