Name: ______________________________________ Use Rstudio Question 1: According to an exit poll for an election, 462 voters of the sample size of 839 reported voting for a specific candidate. You are in charge of constructing a test that the population proportion who voted for this candidate was 0.5 against the alternative that it differed from 0.5. 1) What is the variable of interest? Is it categorical or quantitative? 2) Develop the hypotheses (Provide distinctively all the four steps) 3) If the candidate asks you whether or not she should write an acceptance speech, what would you advise her? Explain your reasonning. Question 2: A cognitive therapy for anorexia was tested on 15 girls. The weight gain of the 15 girls had a sample mean of 6.41 and a standard deviation of 11.62. 1) Using the hypotheses of Ho: =0 and Ha: >0 about the population mean weight gain, and a signifiacance level 0.1, do you have enough evidence that the cognitive therapy worked? Provide all the four steps. 2) If the decisicion in (1) is an error, what type of error is it? 3) Explain in context the consequences of committing that type of error. Problem 3: Your friend claims that the selling price of a PDA (Personal Digital Assistant) is more that $265. In order to prove his case, he collected the prices from eighteen randomly chosen stores, and the data are shown below: 251; 245; 259; 207; 214; 240; 229; 259; 233; 245; 218; 176; 251; 240; 236; 229; 245; 229 1) Construct and interpret in context the 90% confidence interval. 2) Does your friend claim hold? Explain. 1 Problem 4: A researcher predicts that the percentage of people who watch TV is lower now than before the advent of the Internet. According to the General Social Survey, 57 of 1483 subjects sampled in 1975 and 87 of the 1324 subjects sampled in 2008 reported watching NO TV. 1) Carry out the test. Show EXPLICITLY all steps of a significance test ( = 0.05). 2) Explain whether the results support the research claim. 3) If you were to construct the 95% confidence interval comparing the proportions, would it contain 0? Explain how you know based on the results of parts 1) and 2) without actually finding the interval. 2