The confidence level indicates how confident you want to be that the interval estimate you construct actually contains the population parameter of interest. The following applet allows us to experiment with different sample sizes and condence levels to better demonstrate its effect on confidence intervals. The applet will simulate the process of repeatedly taking a random sample and computing a corresponding condence interval. Go to the website (http://digitalrst.'oprub.com/stats_applet/stats_applet_20_ciprop.html). Read the description of the applet. a. Keep p : .5. Select a confidence level of 80% and make the sample sizen : 50. Simulate 25 samples (do this by clicking on "sample 25" a few times). What is your percent hit? b. Reset the applet. Now select the sample size to hen = 5. Simulate 25 samples (do this by clicking on "sample 25" a few times). What is your percent hit? Is the percentage of captures larger or smaller than when n = 50? If a difference, why do you think this difference in performance is occurring? Explain. Question 3: You wish to estimate the proportion of fatal accidents that are alcohol related at a 99% level of confidence. Find the minimum sample size needed to be accurate to within 2% of the population proportion. Use a preliminary estimate of p = 0.235. Question 4: In a survey of 190 college students, 134 students said they believe there is extraterrestrial life. Assume the sample is representative of the population. a. Find a 95% confidence interval for the proportion of all college students who believe there is extraters restrial life. b. Write a sentence that interprets the condence interval found in part (a). Question 5: The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 863 patients who received 10 mg doses of Lipitor daily, 47 reported headache as a side effect. The FDA believes that more than 3 percent of consumers of Lipitor will report a headache as a side effect. a. Define the parameter of interest, and identify the claim. b. State the null and alternative hypotheses c. State the Type I error in the context of the question. d. State the Type II error in the context of the question. d. Which error is more serious? Why? Question 6: Computing a confidence interval for p in RStudio The command prop.test(} will provide the confidence interval for p. This command follows the general formula of goal{ - x , data ) where x represents the value of the categorical variable but it will have two additional options: prop.test( ~ 1:. , data , correct=FALSE, conf.leve1 ) It will always have correct=FALSE. The conf .level will always be a number between 0 and 1, and it specifies the confidence level. Further, the categorical variable considered must only have two possible responses, one of which to be viewed as a "Success". For example, recall "The HELP study". This was a clinical trial for adult inpatients recruited from a detoxification unit. Patients with no primary care physician were randomized to receive a multidisciplinary assessment and a brief motivational intervention or usual care, with the goal of linking them to primary medical care. The data set has many variables, but here we will only use housing. The variable housing