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October 5th, 2008, 06:59 AM  #1 
Newbie Joined: Oct 2008 Posts: 1 Thanks: 0  Use a critical value to test H0 versus Ha
Hi, using a random sample of 100 measurements to test H0 µ=80 versus Ha µ<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. 
October 10th, 2008, 08:10 PM  #2 
Newbie Joined: Oct 2008 Posts: 4 Thanks: 0  Re: Use a critical value to test H0 versus Ha
To find a critical value, all you do is find the zscore 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 zscore 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 twotailed. That zscore 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 zscore 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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