Week8Recitation_ExploringHTs (1)

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Michigan State University *

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231

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Statistics

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Apr 3, 2024

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docx

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Uploaded by SargentFieldMagpie28

SS24 STT 231: Statistics for Scientists Week 8 Recitation Activity: Exploring hypothesis tests Your name: _______________________________________ Your NetID : _____________________________________ In today’s recitation, you’ll be exploring various properties of hypothesis tests, a class of statistical procedures useful for evaluating claims about the unknown value of a parameter of interest. Investigating tattoos ~ According to a recent poll by Ipsos 1 , 30% of all Americans, regardless of their age, have at least one tattoo. Suppose you want to test the null hypothesis that this figure accurately describes the rate at which MSU students have at least one tattoo, against a two-sided alternative. 1. For exercises (a) and (b), create your own example of a sample of 100 people that satisfies the indicated property. Do this by providing the sample numbers with a tattoo and without a tattoo. Report the test statistic , p-value , and estimated effect size from a one-proportion z-test. Using the blank distribution provided, sketch the results associated with your provided example. a. The two-sided p-value is less than 0.001. X = no. of sampled MSU students with at least one tattoo. Sample size 100 ^ π 0.01 z test statistic 4.3664 p -value 0 Est. effect size ^ h -0.4634 b. The two-sided p-value is greater than 0.20. X = no. of sampled 1 https://www.ipsos.com/en-us/news-polls/more-americans-have-tattoos-today

MSU students with at least one tattoo. Sample size 100 ^ π 0.25 z test statistic -1.091 p -value 0.2752 Est. effect size ^ h -0.1091 c. In exercise (a), you were asked to provide one set of sample results that produce a two-tailed p-value less than 0.001. In the space provided, determine all possible sample values that satisfy this property. so, similarly, anything more than 46 tattooed individuals out of a sample of 100 would produce a p-value below 0.001. → +3.290527 the 0.001/2 quantile ranking: qnorm(0.001/2,0,1) = -3.290527 d. In exercise (b), you were asked to provide one set of sample results that produce a two-tailed p-value greater than 0.2. In the space provided, determine all possible sample values that satisfy this property. range of about 0.2413 to 0.3587. the SE to increase by a factor of √ 2 e. Consider the solution you created for (a), which asked you to develop a hypothetical set of sample results that would produce a two-tailed p-value less than 0.001 for n = 100 . Suppose instead that n = 50 ; describe how your solution would need to change to continue to meet the requirements in (a). 0.5133 f. Consider the solution you created for (b), which asked you to develop a hypothetical set of sample results that would produce a two-tailed p-value greater than 0.2 for n = 100 . Suppose that it was additionally required that | ^ h | ≥ 0.5 . Would your solution have to change? If so, provide your updated solution below OR demonstrate that it is not possible to meet both requirements at the same time for n = 100 .

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