lecture_8_1 - — reminder And as always if the p-value is...

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    Inference for proportions Significance test for proportions IPS chapter 8.1 © 2006 W.H. Freeman and Company
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The sampling distribution of a sample proportion is approximately normal (normal approximation of a binomial distribution) when the sample size is large enough. p ˆ
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Significance test for  p The sampling distribution for is approximately normal for large sample sizes and its shape depends solely on p and n . Thus, we can easily test the null hypothesis: z = ˆ p - p 0 p 0 (1 - p 0 ) n If H 0 is true, the sampling distribution is known The likelihood of our sample proportion given the null hypothesis depends on how far from p 0 our is in units of standard deviation. This is valid when both expected counts—expected successes np 0 and expected failures n (1 − p 0 )—are each 10 or larger. p 0 (1 - p 0 ) n p 0 ˆ p p ˆ p ˆ
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P-values and one or two sided hypotheses
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Unformatted text preview: — reminder And as always, if the p-value is smaller than (or equal to) the chosen significance level α , then the difference is statistically significant and we reject H . A national survey by the National Institute for Occupational Safety and Health on restaurant employees found that 75% said that work stress had a negative impact on their personal lives. You investigate a restaurant chain to see if the proportion of all their employees negatively affected by work stress differs from the national proportion p = 0 . 75. H : p = p = 0.75 vs. H a : p ≠ 0.75 (2 sided alternative) In your SRS of 100 employees, you find that 68 answered “Yes” when asked, “Does work stress have a negative impact on your personal life?” Is this result significant at the 5% level?...
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