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Asked Apr 2, 2019
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Hello. Can I get help on how to work out this problem? If there is also a way to calculate using the TI-83 graphing calculator, that would be helpful. Thanks!

 

Suppose that you have a population that is normally distributed with a
standard deviation of 120, and you want to test Ho : μ-1,000 versus
Ha : μ > 1,000, at the level α 0.05. You draw a random sample
alternative Ha : μ
1020?
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Suppose that you have a population that is normally distributed with a standard deviation of 120, and you want to test Ho : μ-1,000 versus Ha : μ > 1,000, at the level α 0.05. You draw a random sample alternative Ha : μ 1020?

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Step 1

Power of a test:

Power of a test is the probability of rejecting a null hypothesis when it is false. That is, the probability of rejecting a null hypothesis when the alternative hypothesis is true. Therefore,

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Step 2

The null and alternative hypotheses are H0: µ = 1,000 and Ha: µ > 1,000. A random sample of size 36 is taken from the population with standard deviation 120. The power of the test wants to calculate at the alternative Ha: µ = 1,020. The test is right tailed, therefore the critical region for the test is, Z > Za. The significance level is 0.05 and the Z- value corresponding to significance level 0.05 is 1.645. Therefore, the power of the test is given by:

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Step 3

Substituting µ0 = 1,000 and σ = 120, and n=...

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