Box 2 29 Points Box 2 1) What is the purpose of random assignment? A random assignment is an experimental technique that randomly assigns treatments to different groups (units). Using random assignments allow us to eliminate the effects of lurking variables. If there is random assignment we can say that the explanatory variables caused the change in the response variable. 2) What is a possible lurking variable in the \"Music for Studying\" experiment, other than the ones discussed in the activity? Age, type of music being listened to, headphones or no headphones, volume 3) Suppose that there are fundamental differences in the way music affects men and women. Which principle of experimental design will ensure the proportion of men (and women) is exactly equal in the treatment and control groups in the experiment (rather than approximately equal in the long run) if we have 48 men and 42 women in the study? Blocking 4) When working with proportions we investigated the effect of sample size on inference in terms of the width of a confidence interval. Which principle of experimental design discusses this same idea? Replication. It helps to eliminate the lurking variables and by gathering more trials it centers in closer to the mean Does the use of stents reduce the risk of stroke? Stents are small mesh tubes that are placed inside narrow or weak arteries to assist in patient recovery after cardiac events and reduce the risk of an additional heart attack or death. Researchers randomly assigned 224 of the volunteer patients who were deemed to be \"at risk\" to the treatment group which received stents along with medical management (medications, dietary support, etc). The remaining 227 volunteers were assigned to the control group which received the same medical management but did not have stents surgically implanted. The data from 1 year after the study began is displayed in the table below. Treatment Control Total Stroke 45 28 73 No event 179 199 378 Total 224 227 451 5) Is this an experiment or an observational study? Experimental 6) Define a \"success\" as having a stroke. What is the proportion of successes for the treatment group? Proportion who had a stroke in the treatment group: x-bar =45/224=.201 (or 20%) (group with the stent) 7) 1 What is the proportion of successes for the control group? Proportion who had a stroke in the control group: x-bar=28/227=.123 (or 12%) (group without sent) 8) Without conducting a hypothesis test, does it appear that stents reduce the risk of stroke? Explain your reasoning. No. The placement of a stent does not appear to reduce the risk of stroke because those with the stent had an 8% increased chance of having a stroke versus those without the stent. Researchers studying the effect of antibiotic treatment for acute sinusitis compared to symptomatic treatments randomly assigned 166 adult volunteers diagnosed with acute sinusitis to one of two groups: treatment or control. Study participants received either a 10-day course of amoxicillin (an antibiotic) or a placebo similar in appearance and taste. Both groups self-administered acetaminophen and nasal decongestants as desired. At the end of the 10-day period patients were asked if they experienced significant improvement in symptoms. The distribution of responses are summarized below. Significant improvement? Treatment Yes No Total 76 9 85 Control 65 16 81 Total 141 25 166 9) How did the experiment use blinding? Some of the participants used the antibiotic and some received a placebo without knowing which was the actual medication because both the antibiotic and placebo were similar in appearance and taste. 10) What is the explanatory variable? Is it categorical or quantitative? (2 points) Explanatory: which medication did they receive? Categorical 11) What is the response variable? Is it categorical or quantitative? (2 points) Responsive variable: Did their symptoms improve? Categorical 12) Compute the proportion improved for the treatment group. Use proper notation. Define the treatment group as group 1. P1-hat= 76/85=.894 13) Compute the proportion improved for the control group. Use proper notation. Define the control group as group 2. P2-hat=65/81=.802 14) Compute the overall proportion to improve. Use proper notation. Pt-hat =141/166=.849 where \"t\"=total 15) Find the difference in proportion to improve for the treatment group minus the control group. Use proper notation. P1-hat minus P2-hat .894-.802=.092 Box 2 29 Points 16) What is the null hypothesis in notation? H not: P1=P2 17) What is the alternative hypothesis in notation? H a: P1>P2 18) Enter these data into our Web Apps for [2 Categ]. Check that the proportion in each group match your answers to 12-13. Then click [Test] and obtain at least 5001 samples. Find the p-value. Take a screenshot and paste it here. (The P-value was calculated after I took the screen shot) Count values equal to or greater than .092 gave me a P-value of 0.03099 19) How is one dot on the randomization distribution created? Using cards I would: NOT SURE HOW I AM TO WORD THE CARDS Shuffle the cards and separate them into two piles of 83 each Collect the data of improved and not improved The difference p1-hat minus p2-hat=1dot on the graph I would then do this 165 more times to create the rest of the graph 20) Where is the distribution centered? Why? (2 points) The distribution is centered on the null because we are assuming the null hypothesis to be true. 21) Write a conclusion based on your p-value found in 18. A P-vlaue of 0.0309 showed strong evidence against the hull hypothesis. Amoxicillin (the antibiotic) improved symptoms of acute sinusitis in this sample (NOT in the population). 22) What is the scope of inference for this study? 1. Were the cases randomly selected from the population? 3 No because there were volunteers 2. Were cases randomly assigned to treatments? Yes, they were randomly assigned A survey was conducted on 218 undergraduates from Duke University who took an introductory statistics course in Spring 2012. Among many other questions, this survey asked them about their GPA and the number of hours they spent studying per week. 23) Is this an experiment or an observational study? Observational 24) What is the response variable for this study? GPA 25) What is the explanatory variable? Number of hours spent studying per week 26) The survey showed that people who studied more had higher GPAs. Can we conclude that studying for a longer time will cause a higher GPA? Explain your reasoning. Not necessarily. Because this is an observational study, we cannot imply a causal relationship between earning a higher GPA because of studying longer. Remember to turn in as a PDF