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Central Limit Theorem tell us about this value relative to the true mean net worth in the US population? 2. Hypothesis Testing You are interested in knowing whether the share of people who smoke is the same in California and Florida. You collect a random sample of 1,000 California residents and 900 Florida residents. You ask each of them whether they smoke or not and create a binary (dummy) variable smoke 1 if they say Yes and smoke 0 if they say No a) Write the Stata command you would use to find the mean and standard deviation in smokers for each state Using the command you mentioned above, you find the following: Descriptive Statistics for Smoke Variable in each Sample Obs 1,000 900 State Mean 0.15 0.20 Std. Dev 0.24 0.21 Min. 0 0 Max California Florida Construct the 90% confidence interval for the share of smokers in California. Construct the 90% confidence interval for the difference in the share of smokers between California and Florida. b) c)d) Test the null hypothesis that the share of smokers in California and Florida are the same against the lternative that there are less smokers in California. The following questions refer to this test: i. State the null and alternative hypotheses in equation form. ii Calculate the t-stat. iii. What are the degrees of freedom for this test? iv. Do you reject this null hypothesis at a 5% significance level? State your answer as a full sentence (i.e. Yes, I reject this null or no, I... How did you reach this conclusion (i.e. what rejection rule did you use?) v. Based on your answer to 2.d.iv, is the p-value for this test greater or smaller than 0.05? vi. Do you reject this null hypothesis at a 1% significance level? State your answer as a full sentence (ie, Yes, I reject this null or no, I... How did you reach this conclusion (i.e. what rejection rule did you use?) e) The graph below shows a Student-t distribution with 899 degrees of freedom. a. Shade, using vertical lines, the rejection region for α-190 for a one-sided test. b. Shade, using horizontal lines, the rejection region for-5% for a one-sided test. c. Indicate, with a horizontal line, the approximate one-sided p-value for the t-stat calculated in question 2.d.ii. 0.4 5 0.3 5 0.2 0.15 0.1 0.05 0 -3 -2 -1 0 2

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Focali texnia. са с 1 а caasas ARUS euaeesas ase X2 = 0.20 6,- 0.2 EEROARd ERCARE o Confidence inlcrval 4O4 = 0.15十e--oo393で0.01245 e 539 6 245 j), . go% confidence inter al is 13602 ið go % confide uce îWerval firm difference- ratre.rame 干ホー 2. O, 15-0.20 lOoO 900 o.05 +0.0163 E O 33] ว่า 2 0.O5 -....o. 이63 -O-066g = G Confidence temean differe.nce.

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