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Economics 105: Statistics

Economics 105: Statistics. Go over GH 9 & 10 GH 11 and 12 due Tuesday. 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)

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Economics 105: Statistics

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  1. Economics 105: Statistics Go over GH 9 & 10 GH 11 and 12 due Tuesday

  2. 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

  3. 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

  4. Hypothesis Testing

  5. 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 )

  6. 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. What are the consequences of Type I and Type II errors?

  7. 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.

  8. What are the appropriate H0 & H1? • The Math & Science Center improves exam scores. • A professor would like to know if having a stats lab increases student grades relative to a class without a lab. • A firm that sends out advertising flyers wants to convince potential customers (i.e., firms) that it can increase their advertising response rate.

  9. 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.

  10. 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.

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