Upload
halien
View
222
Download
5
Embed Size (px)
Citation preview
155S8.2.notebook
1
March 29, 2010
Oct 268:10 PM
MAT 155DY1 & DY2Chapter 8 Hypothesis Testing8.2 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
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.
See "S4D.1 MAT 155 Chapter 8 Hypothesis Testing" in Course Documents of CourseCompass.
155S8.2.notebook
2
March 29, 2010
Oct 268:10 PM
Statdisk: Hypothesis Testing
Oct 268:10 PM
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.
Section 8.2 Basics of Hypothesis Testing
155S8.2.notebook
3
March 29, 2010
Oct 268:10 PM
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.
Section 8.2 Basics of Hypothesis Testing
Oct 268:10 PM
418/10. Express the null hypothesis and alternative hypothesis: Most households have telephones.
Section 8.2 Basics of Hypothesis Testing
155S8.2.notebook
4
March 29, 2010
Oct 268:10 PM
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.
Section 8.2 Basics of Hypothesis Testing
Oct 268:10 PM
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%.
Section 8.2 Basics of Hypothesis Testing
155S8.2.notebook
5
March 29, 2010
Oct 268:10 PM
418/19. Find the critical z values. Assume normal distribution. Righttailed test; alpha = 0.01.
Section 8.2 Basics of Hypothesis Testing
Oct 268:10 PM
418/20. Find the critical z values. Assume normal distribution. Lefttailed test; alpha = 0.05.
Section 8.2 Basics of Hypothesis Testing
155S8.2.notebook
6
March 29, 2010
Oct 268:10 PM
418/24. Find the critical z values. Assume normal distribution. alpha = 0.005; H1: p not = 0.2.
Section 8.2 Basics of Hypothesis Testing
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
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.
Section 8.2 Basics of Hypothesis Testing
155S8.2.notebook
7
March 29, 2010
Oct 268:10 PM
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.
Section 8.2 Basics of Hypothesis Testing
Oct 268:10 PM
419/30. Find the Pvalue. The test statistic in a lefttailed test is z = 2.00.
Section 8.2 Basics of Hypothesis Testing
155S8.2.notebook
8
March 29, 2010
Oct 268:10 PM
419/34. Find the Pvalue. H1: p not = 0.667, test statistic is z = 2.05.Section 8.2 Basics of Hypothesis Testing
Oct 268:10 PM
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.
Section 8.2 Basics of Hypothesis Testing
155S8.2.notebook
9
March 29, 2010
Oct 268:10 PM
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.
Section 8.2 Basics of Hypothesis Testing
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.