TA Section 4, ECN102 2015 Spring Ilhyun Cho∗ April 22, 2015 Central Limit Theorem Let X = 1 if the toss of a six-sided die yields a five or six, and let X = 0 otherwise. Then P r[X = 1] = and P r[X = 0] = 23 1 3 • Obtain µ = E[X] from first principles. µ = E[X] = 2 1 1 ∗ 0 + ∗ 1 = ≈ 0.3333 3 3 3 • Obtain σ 2 = E[(X − µ)2 ] from first principles. σ 2 = E[(X − µ)2 ] = 2 1 1 4 2 ∗ + ∗ = ≈ 0.2222 3 9 3 9 9 Suppose for X ∼ (µ, σ 2 ) like above, we form 10,000 samples of size 100 and obtain 10,000 sample means. • What approximately do you expect the average of the x ¯ to equal? 0.3333 • What approximately do you expect the variance of the x ¯ to equal? 0.0022 • What approximately do you expect the standared deviation of the x ¯ to equal? 0.0471 Statistical Inference Suppose Keita argues that the average UC Davis students’ housing rental fee is $450 per month. Ilhyun wants to check whether his argument is true or not. Ilhyun surveyed 100 students’ housing rental fee per month randomly in 2014 spring quarter. The sample mean is $500 and sample standard deviation is $250. Can you reject the null hypothesis at the five-percent level of significance? H0 : The average students’ housing rental fee is $450. H1 : The average students’ housing rental fee is not $450. t= x ¯−µ √s n ∼ T (n − 1) Under H0 , t= 500−450 √250 100 =2 Test statistic = |2| > 1.984217 = critical value. Thus, reject H0 dis invttail(99, 0.025) = 1.984217 ∗ [email protected], office hours: Wednesday 9:00 am - 11:00 am , 115 SSH. 1

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