Discussion #8 (due 6/17) Hypothesis Tests Applying Hypothesis Tests 1. How would you explain to someone who doesn't understand statistics the difference between confidence intervals and hypothesis testing? 2. Find a research article that uses a hypothesis test. Give either the reference for it or the website address at which you found it. Discuss what the research was trying to show, as well as the results from the test. Note that others have not read your article so you'll need to give a little bit of background information. Discussion #9 (due 6/19) 1. You are conducting a hypothesis test, just as we did in module 8. How do the tests you just learned about differ from those in module 7? 2. Give an example of two categorical variables that you believe would be dependent on each other. 3. Give an example of two categorical variables that you believe would be independent of each other. Quiz 7 (due 6/18) 1. A student at a university wants to determine if the proportion of students that use iPhones is less than 0.44. If the student conducts a hypothesis test, what will the null and alternative hypotheses be? 2. Consumers Energy states that the average electric bill across the state is $38.35. You want to test the claim that the average bill amount is actually different from $38.35. What are the appropriate hypotheses for this test? 3. I am interested in the average number of hours of sleep students get per night. Specifically, I want to know if the average number of hours of sleep students get is less than 8 hours per night, since 8 hours of sleep per night is what is recommended. I ran this test in R and the output is below: > t.test(sleep.night, mu=8, alternative = "less") One Sample t-test data: sleep.night t = -1.7774, df = 26, p-value = 0.0436 alternative hypothesis: true mean is less than 8 95 percent confidence interval: -Inf 7.966877 sample estimates: mean of x 7.179894 Based on the pvalue given, what conclusion would you make at the 5% significance level? 4. A chemist is interested in the amount of impurities in a liquid that she could produce by a chemical process. She was concerned that the liquid would not be satisfactory for use if the impurity level went above 12. To test her process of making the liquid, she made 9 samples of the liquid and found the sample impurities had an average of 17 with a SD of 6. Carry out a test of the hypotheses Ho: < 12 vs. H1: > 12, where u is the average impurity level for her process. 5. A student leader believes that 60% of the students oppose a development at Asylum Lake. To check this claim a survey of 200 students is carried out. It was found that 100 students in the sample opposed Asylum Lake development. Is there enough evidence to reject the student leaders belief? Include your hypotheses, test statistic, pvalue and conclusion