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October 5th, 2008, 06:59 AM   #1
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Use a critical value to test H0 versus Ha

Hi,

using a random sample of 100 measurements to test H0 =80 versus Ha <80 if the mean sample = 85 and the variance = 20

Use a critical value to test H0 versus Ha by setting alpha equal to .10


I am not sure how to find the critical value..In the question before this one I found out that the Z value was = to 0.025 by using the Z equation.

So i just need to know how to do the step in bold.
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October 10th, 2008, 08:10 PM   #2
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Re: Use a critical value to test H0 versus Ha

To find a critical value, all you do is find the z-score that correlates with the number given. An example is if the problem asks you to be 95% confident that your mean will fall between two extremes (that's what a confidence interval is), you would find the z-score that is at the 95 and 5 percentiles (0 + .025 and 1 - .025). That totals to 5% or 95% certainty. This works if your distribution is two-tailed. That z-score is plus or minus 1.96.

Confidence Level: 90%, 95%, 99%
alpha: 0.10, 0.05, 0.01
Critical value: 1.645, 1.96, 2.575

The confidence level is given. The alpha is 1 - the confidence level. The critical value is the z-score that correlates with the probability.

Now, I think you're doing hypothesis testing. Those will vary based on whether your alternate hypothesis has a > or < sign and an = sign (divide by 2 with an equal sign, or do a greater or less than without dividing by two.)
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