STAT 13 In-class Week 4 Activity (2)

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STAT 13 In-Class Activity: Fall 2022 Week 4 Name:_________________________ SID:_______________________ Section:____ 2.1.5* True or false? A. Random samples only generate unbiased estimates of long ‐ run proportions, not long ‐ run means. B. Nonrandom samples are always biased. C. There is no way that a sample of 100 people can be representative of all adults living in the United States. 2.1.6 When stating null and alternative hypotheses, the hypotheses are: A. Always about the parameter only B. Always about the statistic only C. Always about both the statistic and the parameter D. Sometimes about the statistic and sometimes about the parameter 2.1.7* When using simulation ‐ or theory ‐ based methods to test hypotheses about a proportion, the process of computing a p ‐ value is: A. Different if the sample is from a process instead of from a finite population B. The same if the sample is from a process instead of from a finite population C. Sometimes different and sometimes the same if the sample is from a process instead of a finite population 2.3.5* Suppose that you perform a significance test and, based on the p ‐ value, decide to reject the null hypothesis at the α =0.01 significance level. Then suppose that your colleague decides to conduct the same test on the same data but using a different significance level. For each of the following significance levels, indicate whether you would reject the null hypothesis, fail to reject the null hypothesis, or do not have enough information to say. ( Hint: First ask yourself what must be true about the p ‐ value.) 1. α =0.10 2. α =0.05 3. α =0.0001 4. α =0.065 2.3.6* Suppose that you perform a significance test using the α =0.05 significance level. 1. For what p ‐ values would you reject the null hypothesis? 2. For what p ‐ values would you fail to reject the null hypothesis? Campus newspaper* 2.3.17 Suppose that you are considering whether to publish a weekly alternative newspaper on campus. You decide to survey a random sample of students on your campus to ask if they would be likely to read such a newspaper. Your plan is to proceed with publication only if the sample data provide strong evidence that more than 10% of all students on your campus would be likely to read such a newspaper. 1. Identify the parameter of interest, in words. 2. Express the appropriate null and alternative hypotheses for conducting this test. 3. Specify what Type I error represents in this situation. Also indicate a potential consequence of Type I error. 4. Specify what Type II error represents in this situation. Also indicate a potential consequence of Type II error. r

3.1.1* Let π denote some population proportion of interest and suppose a 95% confidence interval for π is calculated to be (0.6, 0.7). Also, suppose that we want to test H 0 : π =0.63 vs. H a : π≠0.63 What can you say about the corresponding p-value? A. The corresponding p-value will be smaller than 0.05. B. The corresponding p-value will be larger than 0.05. C. Need more information to answer this. 3.1.3* Let ππ denote some population proportion of interest and suppose a 95% confidence interval for ππ is calculated to be (0.63, 0.73) and a 99% confidence interval for π is calculated to be (0.61, 0.75). Also, suppose that we want to test H 0 : π =0.74 vs. H a : π≠0.74 What can you say about the corresponding p-value? A. The corresponding p-value will be smaller than 0.05 but larger than 0.01. B. The corresponding p-value will be larger than 0.05. C. The corresponding p-value will be smaller than 0.01. D. I can’t say anything about the corresponding p -value until I run the test. Studying statistics* 3.3.8 In a precourse, anonymous survey of students in her introductory statistics course, one of the authors asked her students how many hours per week they expected to spend studying statistics outside of class. Forty-nine students responded to that question, with an average of 8.2 hours and a SD of 3.79 hours. The data were not strongly skewed. 1. Identify the observational unit for this study. 2. Identify the variable of interest and whether it is categorical or quantitative. 3. Use the Theory-Based Inference applet to calculate and report the 95% confidence interval for the parameter of interest. 4. In the context of this study, was it valid to use the theory-based ( tt -distribution) approach to find a confidence interval? Explain your reasoning. 5. Interpret the 95% confidence interval reported in part (c) in the context of the study.

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