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Lecture 6

ADM2304 Lecture 6: 6
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Department
Administration
Course
ADM2304
Professor
Tony Quon
Semester
Fall

Description
Comparing Non-Independent Proportions from the Same Sample: —> proportions are not independent so we cannot ignore the covariance factor variance of the sample difference however now as a covariate term:
 e.g, in a sample of 1,000 respondents 39% indicated support for the Conservatives and 34% indicated support for the Liberals. Can we state that there is a real difference between the two at a significance level of 5%? H : p − p = 0 0 C L —> Therefore we do not reject the null hypothesis, H : p − p ≠ 0 a C L 1.85 is less than 1.96 (the 95% shit). There is ˆ ˆ (.39*.61+.34*.66+2*.39*.34 ) insufficient evidence to suggest that there is a real SE(p −1p ) 2 =.027 difference between the Liberal and Conservative 1000 .39−.34 support ⇒ z = =1.85< z =1.96 .027 .025 Comparing Two Means From Independent Populations: Interested in:µ1− µ 2 Pointestimate : x −1x 2 Comparing Two Populations: Mean(x −1x )2= Mean(x )−1Mean(x ) = 2 − µ1 2 Var(x 1 x 2 =Var(x )1Var(x ) 2 since independent 2 2 σ 1 σ2 = + n1 n2 2 2 2 2 ⇒ SD(x − x ) = σ 1 + σ2 and SE(x − x ) = s1 + s2 1 2 n n 1 2 n n 1 2 1 2 —> We can assume that the distribution of the difference between the two sample means is normal —> If we don’t know the population SDs and use instead the sample SDs then we can use the t-distribution instead Comparing Two Populations: —> Suppose we are interested in determining whether there is a statistical difference between the means of two populations. Thus H : µ - µ = µ a0d H1: µ 2 µ ≠ 0 . Then tae t1o sa2ple t0 test uses the test statistic: Three options for the degrees of freedom: 1. The conservative approach: take the minimum of n1 - 1 and n2 - 1. Why is this conservative? 2. Compute from the data directly: 3. If original population is not too skewed and bo1h n > 30 a2d n > 30 O1 n > 100 and2n > 100 then approximate by using the standard normal distribution instead Comparing Two Populations: H :µ −µ ≠µ P-value = 2×Pr t > t a 1 2 0 ( stat or H :µ −µ > µ P-value = Pr t > t a 1 2 0 ( s
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