Hypothesis Testing-Z-Test

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  • 1. OPENERPlease find the critical value(s) for eachsituation and draw the appropriatefigure, showing the critical region:a. Two-Tailed Test=0.05b. Right-Tailed Test=0.02c. Left-Tailed Test =0.01

2. Homework Learning GainsLesson 12 3456789Gain81.6 - - 92.0 77.5 OpenerCloser Opener Closer OpenerCloser Opener Closer OpenerCloser Opener Closer Opener81.4 94.081.9 90.0 - 65.0 - 90.0 3. Speaking of Homework / Grades Check Edbox Not everyone has handed in theirhomework calendars for Ch. 8 Barring any discussed changes to your grade, what you see on Edbox is an accurate reflection of what will go home with your quarter grades. 4. Review A statistical test uses the dataobtained from a sample to make adecision about whether the nullhypothesis should be rejected. The numerical value obtained from astatistical test is called the test value. 5. Review The critical value separates thecritical region from the noncriticalregion. The critical region is the range ofvalues of the test value that indicatesthat there is a significant differenceand that the null hypothesis shouldbe rejected. 6. Two Tailed v. Left/Right-Tailed TestTwo-Tailed=0.10 NonCriticalRegionCritical RegionCritical Region/2=0.05/2=0.05 CV=-1.65CV=1.65 Critical ValueCritical ValueLeft-TailedRight-Tailed=0.05Non=0.10 Non CriticalCritical RegionRegionCritical Region Critical Region=0.05=0.10CV=-1.65CV=1.28Critical ValueCritical Value 7. Five Steps in Hypothesis Testing1. State the hypotheses and identify the claim.Make sure to use proper symbols.Please include proper units when given.2. Find the critical value(s).Include a diagram that displays all the pertinent information.3. Compute the test value.Include the proper formula.Round properly.Locate and place test value on the diagram.4. Make the decision to reject or not to reject the null hypothesis.Use a complete sentence.5. Summarize the result.Use complete sentence(s) that states the final conclusion clearly in the context ofthe problem.Use the proper vocabulary and statistical terms.Include the proper units if they are given. 8. Section 9-3Z-Test for a Mean 9. When to Use the z Test The z test is a statistical test forthe mean of a population. It canbe used when n> 30 or when thepopulation is normally distributedand is known. 10. Formula for the z Test X z n 11. Hypothesis TestingTraditional Method 12. Example 9-3 A researcher reports that the average salary of assistantprofessors is more than $42,000. A sample of 30 assistantprofessors has a mean salary of $43, 260. At = 0.05, testthe claim that assistant professors earn more than $42,000a year. The standard deviation of the population is $5230. Non RejectionRegion H0: $42,000 H1: >$42,000 (Claim) 13. Example 9-3 A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistantprofessors has a mean salary of $43, 260. At = 0.05, test the claim that assistant professors earn more than $42,000 ayear. The standard deviation of the population is $5230.Step 3:X 4 3, 2 6 0 4 2, 0 0 0zz z 1 .3 2 5230n 30Step 4:Right-TailedDo Not Reject the null hypothesis. Non RejectionStep 5: RegionThere is not enough evidence tosupport the claim that assistant Critical Regionprofessors earn more on averagethan $42,000 a yearCV=1.65 z 1 .3 2 14. Example 9-4 A researcher claims that the average cost of mens athleticshoes is less than $80. He selects a random sample of 36 pairsof shoes from a catalog and finds the following cost (in dollars).(The costs have been rounded to the nearest dollar.) Is thereenough evidence to support the researchers claim at = 0.10?Reference Page 351 for costs.NonRejection Region H0: $80 H1: