# 3-2-09 - 1-tailed test o If it’s not equal to...

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Economics Statistics – Class Notes – 3/2/09 NO MORE PROOFS Application of concepts now Hypothesis Testing Case 1 – A Test on the Population Mean (u) with Standard Deviation (o) known 1. An appropriate null and alternative hypothesis Ho: u = u0 = 10 H1: u > 10 2. A suitable test statistic What would make Xbar normal: If the parent population is normal Or if the conditions of the Central Limit Theorem hold

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3. Find the rejection region – If the alternative hypothesis is true, (Xbar – u) will be large and positive . Hence, the rejection region is in the right tail of Z. 4. Calculate Z – Usually he will present step 4 in step 2 (a time saver!) 5. Decide and interpret in the CONTEXT of the problem. a. If you do not do this, you will lose at least 2 points.
In regards to finding the critical region o If it’s a greater than inequality (right tail 1-tailed test) o If it’s a less than inequality (left tail
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Unformatted text preview: 1-tailed test) o If it’s not equal to inequality (both tails two-tailed test) • The null hypothesis must ALWAYS HAVE SOME FORM OF EQUALITY (Equal, greater than or equal to, less than or equal to) • The Z-critical or rejection region These are values that are consistent with the alternative hypothesis • Type I error – (alpha)% of the time we reject the null hypothesis when the null hypothesis is true • Type II error – (alpha)% of the time we fail to reject the null hypothesis when the null hypothesis is false. FOR ALL CONFIDENCE INTERVALS, WRITE THE FOLLOWING: KEY IMPORTANT WRITTEN PART : Since the value for the test statistic lies in the critical region, we reject the null hypothesis { place context of problem here } [In this case, the null hypothesis is that the number of defects is 40]...
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## This note was uploaded on 06/03/2009 for the course ECON 203 taught by Professor Casler during the Spring '09 term at Allegheny.

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3-2-09 - 1-tailed test o If it’s not equal to...

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