Lecture_22,_Chap_10,_Sec_4_&amp;_6

# Lecture_22,_Chap_10,_Sec_4_&amp;_6 - Chapter 10 Section...

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Chapter 10 Section 4 Testing Claims about a Population Proportion

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Population Proportion Testing Learning objectives Test a claim about a population proportion using the normal model Test a claim about the population proportion using the binomial probability distribution (optional) 1 2
Population Proportion Testing n x p ˆ = In a sample of size n , with x successes, the best estimate of the population proportion is Similar to tests for means, we have Two-tailed tests Left-tailed tests Right-tailed tests

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Population Proportion Testing If: np (1 – p ) ≥ 10 and n ≤ .05 N then the sample proportion is approximately normally distributed
Population Proportion Testing Because we assume that the null hypothesis ( p = p 0 ) is true, we should use for the standard error of the sample proportion Then the test statistic is n ) p ( p 0 0 1 - n p p p p z ) 1 ( ˆ 0 0 0 0 - - =

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Population Proportion Testing We can perform our hypotheses for tests of a population proportion in the same way as the hypothesis tests of a population mean Two-tailed Left-tailed Right-tailed
Population Proportion Testing The process for a hypothesis test of a proportion is Set up the problem with a null and alternative hypotheses Collect the data and compute the sample proportion Compute the test statistic n p p p p z ) 1 ( ˆ 0 0 0 0 - - =

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Population Proportion Testing Either the Classical and the P-value approach can be applied to make a decision Classical approach P -value approach
Population Proportion Testing Problem 1 A researcher believes that less than 60% of students prefer hamburgers over hot dogs. A random sample of 200 students found that 102 of them preferred hamburgers. At α = 0.05, do we have sufficient evidence to support the belief?

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