Stat 2, Summer Session Assignment 6 Name: ___________________________ Student ID: _______________________ Instructions: YOU MUST SHOW ALL YOUR WORK TO RECEIVE FULL CREDIT. You will need a calculator and the normal table in the back of your textbook to do this assignment. If the value you need is in between two values in the normal table, use the one that is closest. 1. A student carries out a survey of UC Berkeley undergraduates by standing in a heavily trafficked area near Sather Gate one Monday afternoon and asking questions of the first 100 people who are willing to talk to him. Is this survey method like taking a simple random sample of all UC Berkeley undergraduates? Explain why or why not. If there is a potential for bias, name which types of bias you are most concerned about, and explain why. 2. A researcher is interested in whether heavy marijuana use can increase the likelihood of developing schizophrenia in young adults who have a family history of schizophrenia. She starts her research by personally interviewing 100 young adults with a family history of schizophrenia and asking them about how frequently they use marijuana. Assuming that the 100 young adults she is interviewing are representative of the population of young adults she is interested in, what other type of bias might we be concerned about here? What kind of influence could this bias have on her conclusions about the percent of young adults with a family history of schizophrenia who smoke every day? this method is not like taking a simple random sample because it's possible that there is selection biasnon response or a comrence sample because he's only asking questions to students who are willing to respond also it might bea conveniencesample because he's only surveying one location at a certain time and day these are a concern bis it can slow the survey by excluding the opinions of those who didn't answer or were not inthe area during the time ofthe survey so it'snot representative ofthe population as a random sample would response bias ble it's likely that there willbe teenage who will inaccurately their usage this bias could mate the percentage smaller therefore affecting the common between the heavy marijuana usage and schizophrenia
3. Several local universities hire a polling company to study how widespread cheating is in online courses. For each of the challenges listed below that this company faces, fill in the blank with the number matching the type of bias this challenge would make us worry about the most. Each type of bias will be used exactly once. (a) Students don't want to admit that they cheat and might lie about it. _________ (b) The company doesn't have contact information for all students. _________ (c) The survey the company will administer is optional. _________ Options: 1 - Selection bias 2 - Non-response bias 3 - Response bias 4. A polling company has been hired to estimate the percentage of people who use Twitter among various demographic groups within the U.S. The polling company has already surveyed one thousand people within the ages 18-44. This age group makes up about 36.5% of the overall population of the U.S. Now the polling company wants to survey people ages 45-64, who make up about 26.4% of the overall population of the U.S. Other things being equal, about how many people should they survey in the 45-64 year old group to achieve a similar level of accuracy in their estimates in both age groups? Answer: _____________ people Explain your answer in one sentence: 3 I 2 1000 we need to survey the same absolute sample size bit in the scenario of a big survey likethis what matters is the actual size of the sample and not the native see compared tothe population
5. In a company made up of 30,000 employees, 6,900 (23%) are enrolled in an optional savings program. The company is considering changing the program and decides to first take a poll of 500 randomly selected employees. In this problem we will look at the sample percentage of employees who are enrolled in the program. (a) Write down all elements of the box model. (b) The average of the tickets in the box is _______ and the SD is _______. (c) Consider the percentage of employees in the sample who are enrolled in the program. What is its expected value? __________% What is its standard error? __________% (d) Use the normal approximation to calculate the chance that the percentage of employees in the sample who are enrolled in the program is between 22% and 24%. Answer: _____________% (e) How do you justify using the normal approximation in (d)? (Your answer should include the name of a theorem and one or more numerical comparisons.) 23 1 77 o soo w replacement 23 42 avg 2 0 23 SD V1.23 771 42 23 i m t number in pt B SD ofbox sample size 100 loot 41.77 24 22 1 88 S3 1243331 53 22 24 g Th sa sa CLT justifies normal approximation it the sample size is large enough 1.23111007 23 to l 77 too to large enoughsample size
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