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ch20inferencesonproportionspart2.studentview

ch20inferencesonproportionspart2.studentview - Chapter 20...

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Chapter 20: Inference on Proportions (Part 2) A: Test of Hypotheses on p Given a dichotomous population for A and A'. Suppose the proportion of A’s is p which is unknown. We take a (large) sample of size n, and count the number of A’s in the sample. Let this number be r . Then By the Normal Approximating Binomial Theorem (NABT; see Chapter 11(C)), ) , ( ~ p n Bin r ) , ( ~ ) , ( ~ npq np N p n Bin r approx exact
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By Chapter 19(B), In the last chapter, we denoted the sample proportion, by and noted that is an unbiased estimate of p. Suppose now we wish to test, for a certain given versus Then, under , (1) becomes so that the test statistic Has a standard normal distribution, N(0,1). We accept at α significance level if This is the one-sample normal test for proportions. n r ) 1 ..( ) ......... , ( ~ n pq p N n r approx ) 2 .... ( ˆ n r p = p ˆ 0 p 0 0 : p p H = 0 : p p H A ) , ( ~ ˆ 0 0 0 n q p p N p approx 0 H α z z S T . A H ) 3 ..... ( ˆ 0 0 0 n q p p p z - =
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Example 1 : In a random sample of 150 TV viewers, 63 viewers liked program A. Let p denote the proportion of all TV viewers who liked program A .
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