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TA10 - ECO2121 Methods of Economic Statistics TA10 1 April...

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ECO2121: Methods of Economic Statistics TA10 1 April 2009 1. Hypothesis Testing (continued) Example: 七成學生領袖曾接觸淫褻物 Given n = 324, x = 233, so ̂ = 0.72. 2. Confidence Interval (Two Populations) Motivation: for X ~ Bernoulli( p X ), p X is the only parameter, we can find both point and interval estimates of p X , as well as conduct hypothesis testing for p X . But if Y ~ Bernoulli( p Y ) independently, can we do the same for p X p Y ? Example 1: if among the 324 students, there are 165 males and 159 females, denote X for male and Y for female, so n X = 165 and n Y = 159, and there are 137 males and 96 females who claim they experience pornographic materials in Internet, construct a 95% C.I. for p X p Y . For a large sample, by CLT, ̂ ~ N ( p X , p X q X / n X ) and ̂ ~ N ( p Y , p Y q Y / n Y ) and assume they are independent (valid?), ̂ − ̂ ~ N ( p X p Y , p X q X / n X + p Y q Y / n Y ). Therefore a 95% C.I. for p X p Y is ( ̂ − ̂ ) ± ̂ + ̂ = 137 165 96 159 ± 1.96 137 165 28 165 165 + 96 137 63 137 137 = [0.1313, 0.3217] (Interpretations? Conclusions?) Example 2: Suppose X
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