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Lecture

# Sampling distribution, hypotheses, confidence intervals

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Department
Statistics
Course
STAT 301
Professor
Brett Hunter
Semester
Fall

Description
21 October Comparing 2 population proportions We want to make inferences about π – π , whe1e π 2nd π come fr1m diffe2ent populations Take independent samples Find p ,1the point estimate for π 1 Find p ,2the point estimate for π 2 So p 1 p i2 the point estimate for π - π 1 2 Sampling Distribution When the samples are independently taken and n is large, π , π not extr1me, 2ollowing hold n1π 1 10 n2π 2 10 n1(1 – π 1 ≥ 10 n2(1 – π 2 ≥ 10 π (1−π ) π (1−π ) 1 1 2 2 p1– p ~2N (π – π1, 2 n + n 1 2 Hypotheses Upper Tail: Is π l1rger than π ? 2 H0: π 1 π 2 0 HA: π 1 π > 2 OR H0: π 1 π 2 HA: π 1 π 2 Lower Tail: Is π s1aller than π ? 2 H 0 π 1 π ≥20 H : π - π < 0 A 1 2 OR H 0 π 1 π 2 H A π 1 π 2 Two Tail: Is π d1fferent from π ? 2 H 0 π 1 π 2 0 H A π 1 π 2 0 OR H 0 π 1 π 2 H A π 1 π 2 When we perform a hypothesis test, we assume H is true. 0 So here, we are assuming π = π 1 2 When π = π1, we2can combine the two populations into one where the true proportion is π = π =1π 2 So we can combine our samples into one sample of size n + n , from wh1ch w2 get an p estimate of the overall population proportion (π), denoted p or c
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