9. Alpha level and the critical region Suppose you are conducting a hypothesis t

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9. Alpha level and the critical region Suppose you are conducting a hypothesis test with the null hypothesis Ho:-100 versus the aternative hypothesis H1 : > 100. You collect a sample from the population of interest and calculate your test statistic. Assuming the null hypothesis is true, assume your test statistic is normally distributed such that you can compare its value to the standard normal distribution. , meaning you are conducting a test. Considering the null and alternative hypotheses given, use the Distributions tool to identfly the boundary thart separates the extreme samples from the samples that are consistent with the null hypothesis. Use an an alpha level a .01 To use the tool, slide the orange line until the area in the rejection region equals the an alpha level. Remember that because the alternative hypothesis contains "greater than>), the rejection region will be in the right tail; that s you will reject the null hypothesis for very large values of the test statistic. Distribution Standard Deviation-1.0 0

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Ho: Mu =100

Ha: Mu > 100

1. Your hypothesis test is one tailed test, meaning you are conduting a one directional - test

2. we have alpha = .01

For alpha = .01, we have .005 in each tail as rejection regions

So, by looking up the Z tables we see that the Z value should be +/- 3.2905 for upper and lower tails.

3. Z boundries are Z = 3.2905 and -3.2905

4. The rejection region is therefore : Z>3.2905 and Z<-3.2905

5. If the alpha level decreases, the size of the rejection region decreases, causing the test to become more stringent

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