155S8.2.notebook
March 29, 2010
MAT 155­DY1 & DY2
Chapter 8 Hypothesis Testing
8.2 Basic of Hypothesis Testing
Notes are available in Course Documents of CourseCompass:
S4D.1 MAT 155 Chapter 8 Hypothesis Testing These notes cover the following topics: Basics of Hypothesis Testing; Testing Claim about Proportion; Testing Claim of Mean, σ known; Testing Claim of Mean, σ unknown; Testing Claim about Standard Deviation
Oct 26­8:10 PM
See "S4D.1 MAT 155 Chapter 8 Hypothesis Testing" in Course Documents of CourseCompass.
Remember to always use the alternative hypothesis to determine whether to use a one­tailed (either left or right) or a two­tailed test.
Decision Rule:
For a left­tailed test, reject Ho if test statistic is less than or equal to critical value.
For a right­tailed test, reject Ho if test statistic is greater than or equal to critical value.
For a two­tailed test, reject Ho if test statistic is less than or equal to negative critical value or greater than of equal to positive critical value.
The P­value (or p­value or probability value) is the probability of getting a value of the test statistic that is at least as extreme as the one representing the sample data, assuming that the null hypothesis is true. The null hypothesis is rejected if the P­value is very small, such as 0.05 or less.
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155S8.2.notebook
March 29, 2010
Statdisk: Hypothesis Testing
Oct 26­8:10 PM
Section 8.2 Basics of Hypothesis Testing
417/6. Use the rare event rule and make subjective estimates to determine whether events are likely.
Claim: The majority of people in the 18­29 are bracket voted in the last presidential election, and polls showed that among 1000 voters in the age bracket, 170 voted.
Oct 26­8:10 PM
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155S8.2.notebook
March 29, 2010
Section 8.2 Basics of Hypothesis Testing
418/8. Use the rare event rule and make subjective estimates to determine whether events are likely.
Claim: College students have IQ scores that vary less than the general population for which sigma = 15, and a random sample of 500 college students results in IQ scores with s = 10.2.
Oct 26­8:10 PM
Section 8.2 Basics of Hypothesis Testing
418/10. Express the null hypothesis and alternative hypothesis: Most households have telephones.
Oct 26­8:10 PM
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155S8.2.notebook
March 29, 2010
Section 8.2 Basics of Hypothesis Testing
418/13. Express the null hypothesis and alternative hypothesis: IQ scores of college professors have a standard deviation less than 15, which is the standard deviation for the general population.
Oct 26­8:10 PM
Section 8.2 Basics of Hypothesis Testing
418/16. Express the null hypothesis (H0) and alternative hypothesis (H1): The percentage of workers who got a job through their college is no more than 2%.
Oct 26­8:10 PM
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155S8.2.notebook
March 29, 2010
Section 8.2 Basics of Hypothesis Testing
418/19. Find the critical z values. Assume normal distribution. Right­tailed test; alpha = 0.01.
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Section 8.2 Basics of Hypothesis Testing
418/20. Find the critical z values. Assume normal distribution. Left­tailed test; alpha = 0.05.
Oct 26­8:10 PM
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155S8.2.notebook
March 29, 2010
Section 8.2 Basics of Hypothesis Testing
418/24. Find the critical z values. Assume normal distribution. alpha = 0.005; H1: p not = 0.2.
You may use Table A­2 or the TI calculator.
­z = invnorm(0.0025) = ­2.81. So, critical values are z = ±2.81.
Oct 26­8:10 PM
Section 8.2 Basics of Hypothesis Testing
418/26. Find the test statistic z. The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%), and the sample statistics include n = 580 peas with 152 of them having yellow pods.
Oct 26­8:10 PM
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155S8.2.notebook
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Section 8.2 Basics of Hypothesis Testing
419/28. Find the test statistic z. The claim is that the majority of medical malpractice lawsuits are dropped or dismissed. Given n = 500 lawsuits; 349 dropped or dismissed.
Oct 26­8:10 PM
Section 8.2 Basics of Hypothesis Testing
419/30. Find the P­value. The test statistic in a left­tailed test is z = ­2.00.
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155S8.2.notebook
March 29, 2010
Section 8.2 Basics of Hypothesis Testing
419/34. Find the P­value. H1: p not = 0.667, test statistic is z = 2.05.
Oct 26­8:10 PM
Section 8.2 Basics of Hypothesis Testing
419/38. State the final conclusion, address original claim, in simple nontechnical terms.
Original Claim: The percentage of female coaches is greater than 50%. Initial conclusion: Reject the null hypothesis.
Oct 26­8:10 PM
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155S8.2.notebook
March 29, 2010
Section 8.2 Basics of Hypothesis Testing
419/40. State the final conclusion, address original claim, in simple nontechnical terms.
Original Claim: The proportion of smokers who experience sleeping difficulty is equal to 0.34. Initial conclusion: Reject the null hypothesis.
Use the flow chart "Hypothesis Test: Wording of Final Conclusion."
Does the claim contain equality? YES Go to the right.
Do you reject H0? YES Go to the right. Use Box 1 for the four on right of chart.
Wording of Final Conclusion:
There is sufficient evidence to warrant rejection of the claim that the proportion of smokers who experience sleeping difficulty is equal to 0.34.
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