Hypothesis Testing - Means - S08

Hypothesis Testing - Means - S08 - STAT E-50 - Introduction...

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STAT E-50 - Introduction to Statistics Hypothesis Testing Hypotheses ± The null hypothesis: H 0 : parameter = value ± The alternative hypothesis: H a : parameter = value we would accept if we reject the null hypothesis Plan ± Check the conditions. ± Specify the model you will use to test the null hypothesis. ± Specify the parameter of interest . Mechanics ± Calculate a test statistic from the data. ± Obtain a P-value = the probability that the observed value of the test statistic (or a more extreme value) could occur if the null model were correct. ± If the P-value is small enough, we will reject the null hypothesis. Conclusion ± Statistical conclusion: state the reason you have decided reject or fail to reject the null hypothesis. ± Conclusion in context: write a complete, clear statement explaining what you conclude. Questions about statistical inference to think about when looking at data: 1. Am I surprised? (Should I reject the null hypothesis?) 2. How surprised am I? (What’s the P-value?) 3. What would not surprise me? (Write a confidence interval for the parameter.) A confidence interval proposes a range of plausible values for that parameter, and should almost always accompany a hypothesis test.
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Inferences About Two Proportions Independence assumption: Within each group, the data should be based on results for independent individuals. Conditions: Randomization condition 10% condition Success/failure condition for each sample Independent samples condition The two groups we are sampling must be independent of each other The Sampling Distribution Model for the Difference Between Two Independent Proportions: Page 2 12 ˆˆ pp Provided that the sampled values are independent, the samples are independent, and the sample sizes are large enough, the sampling distribution of is modeled by a Normal model with: mean () ( ) * zS E −± × 11 22 pq SE p p nn −= + and standard deviation μ =− SD p p + When the conditions are met, the confidence interval for the difference of two proportions is: where we find the standard error of the difference, from the observed proportions. The value of z* depends on the level of confidence that you specify.
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1. Researchers at the National Cancer Institute released results of a study that examined the effects of weed-killing herbicides on house pets. (Associated Press, Sept. 4, 1991). Dogs, some of whom were from homes where the herbicide was used on a regular basis, were examined for the presence of malignant lymphoma. Use the following data to estimate the difference between the proportion of exposed dogs that develop lymphoma and the proportion of unexposed dogs that develop lymphoma: Group Sample Size Number with Lymphoma ˆ p Exposed 827 473 Unexposed 130 19 Check the conditions: Randomization condition 10% condition Success/failure condition for each sample Independent samples condition a) Find a 90% confidence interval estimate for the difference in proportions: () 11 22 12 ˆˆ pq SE p p nn −= + ( ) ( ) * pp zS E −± × Minitab output includes: Sample X N Sample p 1 473 827 0.571947 2 19 130 0.146154 Estimate for p(1) - p(2): 0.425793 90% CI for p(1) - p(2): (0.367500, 0.484086) Page 3
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This note was uploaded on 05/20/2008 for the course STAT 50 taught by Professor Weinstein during the Spring '08 term at Harvard.

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Hypothesis Testing - Means - S08 - STAT E-50 - Introduction...

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