Question

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 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 State California Florida Obs 1,000 900 Mean 0.15 0.20 Std. De 0.24 0.21 Min Max

Answer 1

$(a)~Use~"summarize"~command\\ (d)~i.\\ Null~hypothesis,~H_0:\mu_c=\mu_f\\ Alternative~hypothesis,~H_a:\mu_c< \mu_f.\\ where,~\mu_c=population~mean~no.~of~smokers~in~California.\\ \mu_f=population~mean~no.~of~smokers~in~Florida.\\ ii.~Assume~population~standard~deviations~are~equal.\\ Then~we~estimate~this~by~using~pooled~sample~standard~deviation:\\ s=\sqrt{\frac{(1000-1)*0.24^2&plus;(900-1)*0.21^2}{1898}}= 0.2263\\$

$t-stat=\frac{0.15-0.20}{s\sqrt{\frac{1}{1000}&plus;\frac{1}{900}}}= -4.81 \\ iii.~df=1000&plus;900-2=1898\\ iv.~Critical~value=-t_{0.05,1898}=-1.6457\\ Since~t-stat<-1.6457~so~we~reject~H_0~at~level~0.05~and~conclude~that\\ there~are~less~smokers~in~California.$

$v.~p-value=P(t< -4.81 |t\sim t_{1898})=0.0000008 <0.05.\\ vi.~Yes,~since~p-value<0.01. ~I~reject~the~null~hypothesis~at~1\%~level\\ and~we~get~same~conclusion~as~in~iv.\\ e.$

a.

b.

c.