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2. Hypothesis Testing You are interested in knowing whether the share ofpeople who smoke is the same in California and Florida. You collect a random sample of1,000 California residents and 900 Florida residents. You ask each ofthem whether they smoke or not and create a binary (dummy) variable smoke 1 ifthey sayYes and smoke-0if they say No a) Write the Stata command you would use to find the mean and standard deviation in sokers 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 Min Std. Dev 0.24 0.21 Maz eann 0.15 0.20 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 alternative that there are ess smokeis in California. The following questions refer to this test: i. State the nulland altermative hypotheses in equation form ii Calculate thet-stat. ii What are the degrees of freedom for this test? Do you reject this ull hypothesis at a 5% significance lever, State your answer as a full sentence (ie Yes, I reject this nul or no, I ... How did you reach this conclusion i.e. what rejection rule did you use?) v. Based on your answer to 2.div, is thep-value for this test greater or smaller than 0.05? Do you re ect this mil hypothesis at a 1% sıgnificance lever State your answer as a full sentence (ie. Yes, Ireject this nul or no, I. How didyou reach this concdusion i.e. what rejection rule did you use?)

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(a) Use summarize command (d) i Null hypothesis, Ho : μ.-PF Alternative hypothesis. Ha : μ.< μ where, μ.-population mean no. of smokers in California. u-population mean no. of smokers in Florida ii. Assume population standar d deviations are equal Then we estimate this by using pooled sample standar d deviation uve estimate this b soled same deviation (1000 -1)0.24(900 10.212 1898 0.2263

0.15 0.20 _ t-stat = =-4.81 4.81 S1 1000 900 iii. df = 1000 900-2-1898 iv. Critical value--t005.1898 =-1.6457 Since t - stat < -1.6457 so we reject Ho at level 0.05 and conclude that there are less smokers in California.

v. p-value-Plt <-4.81|t ~ t1898) 0.0000008 < 0.05. uí. Yes, since p-value < 0.01. I reject the null hypothesis at 1% level and we get same conclusion as in iv. e.

a.

1% 2.3283 -2 0 2 3

b.

8 5% 8 1.6457 3 2 -1 1 2 3

c.

ご。 p-value -2 0 2 4

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