1 / 16

Economics 105: Statistics

Economics 105: Statistics. Any questions ? GH 11 and GH 12 due on Friday. What is a Hypothesis?. A hypothesis is a claim (assumption) about a population parameter:. Example: The mean monthly cell phone bill of this city is μ = $42.

braima
Télécharger la présentation

Economics 105: Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Economics 105: Statistics Any questions? GH 11 and GH 12 due on Friday

  2. What is a Hypothesis? • A hypothesis is a claim (assumption) about a population parameter: Example: The mean monthly cell phone bill of this city is μ = $42 Example: The proportion of adults in this city with cell phones is π = 0.68

  3. The Null Hypothesis, H0 • States the claim or assertion to be tested Example: The average number of TV sets in U.S. Homes is equal to three ( ) • Is always about a population parameter, not about a sample statistic

  4. The Null Hypothesis, H0 (continued) • Begin with the assumption that the null hypothesis is true • Similar to the notion of innocent until proven guilty • Refers to the status quo • Always contains “=” , “≤” or “”sign • May or may not be rejected

  5. The Alternative Hypothesis, H1 • Is the opposite of the null hypothesis • e.g., The average number of TV sets in U.S. homes is not equal to 3 ( H1: μ≠ 3 ) • Challenges the status quo • Never contains “=” , “≤” or “”signs • May or may not be proven find evidence in favor of H1 • Is generally the hypothesis that the researcher is trying to prove to find evidence in favor of

  6. Hypothesis Testing Process Claim:the population mean age is 50. (Null Hypothesis: Population H0: μ = 50 ) Now select a random sample X = likely if μ = 50? Is 20 Suppose the sample If not likely, REJECT mean age is 20: X = 20 Sample Null Hypothesis

  7. Reason for Rejecting H0 Sampling Distribution of X X 20 μ= 50 IfH0 is true ... then we reject the null hypothesis that μ = 50. If it is unlikely that we would get a sample mean of this value ... ... if in fact this were the population mean…

  8. Level of Significance,  • Defines the unlikely values of the sample statistic if the null hypothesis is true • Defines rejection region of the sampling distribution • Is designated by , (level of significance) • Typical values are 0.01, 0.05, or 0.10 • Is selected by the researcher at the beginning • Provides the critical value(s) of the test

  9. Level of Significance and the Rejection Region a Level of significance = Represents critical value a a H0: μ = 3 H1: μ≠ 3 /2 /2 Rejection region is shaded Two-tail test 0 H0: μ≤ 3 H1: μ > 3 a 0 Upper-tail test H0: μ≥ 3 H1: μ < 3 a Lower-tail test 0

  10. Hypothesis Testing

  11. Type I & II Error Relationship • Type I and Type II errors cannot happen at the same time • Type I error can only occur if H0 is true • Type II error can only occur if H0 is false If Type I error probability (  ) , then Type II error probability ( β )

  12. Hypothesis Testing for  Pharmaceutical manufacturer is concerned about impurity concentration in pills, not wanting it to be above 3%. From past production runs, it knows that the impurity concentration in the pills is normally distributed with a standard deviation () of .4%. A random sample of 64 pills was drawn and found to have a mean impurity level of 3.07%. Test the following hypothesis at the 5% level on the test statistic scale. Perform the test on the sample statistic scale. What is the p-value for this test? Power if true pop mean = 3.1%? p-value is the lowest significance level at which you can reject H0.

  13. What are the appropriate H0 & H1? • The Federal Trade Commission wants to prosecute General Mills for not filling its cereal boxes with the advertised weight. • Toyota won’t accept a shipment of tires from its supplier if the tires won’t fit their cars.

  14. What are the appropriate H0 & H1? • A professor would like to know if having a stats lab increases student grades relative to a class without a lab. • Ballbearings-R-Us won’t accept a shipment of ball bearings if more than 5% of the shipment is defective. • A firm that sends out advertising flyers wants to convince potential customers (i.e., firms) that it can increase their sales.

  15. Hypothesis Testing for  Pharmaceutical manufacturer is concerned about impurity concentration in pills, not wanting it to be above 3%. From past production runs, it knows that the impurity concentration in the pills is normally distributed with a standard deviation () of .4%. A random sample of 64 pills was drawn and found to have a mean impurity level of 3.07%. Test the following hypothesis at the 5% level on the test statistic scale. Perform the test on the sample statistic scale. What is the p-value for this test? Power if true pop mean = 3.1%? p-value is the lowest significance level at which you can reject H0.

  16. Hypothesis Testing for  Using t Pharmaceutical manufacturer is concerned about impurity concentration in pills, not wanting it to be different than 3%. A random sample of 16 pills was drawn and found to have a mean impurity level of 3.07% and a standard deviation (s) of .6%. Test the following hypothesis at the 1% level on the test statistic scale. Perform the test on the sample statistic scale. What is the p-value for this test? Calculate the 99% confidence interval.

More Related