STAT 210 Final Exam | Questions and Answers

STAT 210 Final Exam | Questions and Answers Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. Based on this information, what is the population of interest? All visitors to the Bahamas in 2019. Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. Based on this information, what is the parameter of interest? The proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island A sample of 400 visitors to the Bahamas in 2019 were selected and each was asked whether they spent some time at Atlantis Paradise Island. In this sample, 120 visitors, or 30%, indicated that they spent some time at Atlantis Paradise Island. In this scenario, is 30% an example of a parameter or a statistic? Statistic Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. Based on a brochure published by the resort, the proportion of tourists who visit the Bahamas and spent time at Atlantis Paradise Island is .20. A statement about a population parameter, such as π=.20 is which of the following? Hypothesis Atlantis Paradise Island is an ocean-themed resort on Paradise Island (Links to an external site.) in the Bahamas (Links to an external site.). Of interest is to determine the proportion of all visitors to the Bahamas in 2019 that spent some time at Atlantis Paradise Island. As reported by the department of tourism, the total number of visitors in 2019 was 120,000. In this scenario, is 120,000 an example of a parameter or a statistic? Parameter In partnership with the U.S. Department of Transportation, the Commonwealth of Virginia, the City of Richmond and Henrico County, GRTC and the Project Team launched the GRTC Pulse service on Sunday, June 24, 2018. What type of characteristic is the day GRTC Pulse service was launched? Constant For all passengers who have ridden the GRTC Pulse since service was launched, of interest is to determine the mean age of all the passengers. What type of characteristic is the mean age of all passengers who have ridden the GRTC Pulse? Continuous Quantitative variable As they board, passengers are asked if they live in the City of Richmond, Henrico County, Chesterfield County, Hanover County, or another location (5 options). The location in which a GRTC Pulse passenger lives is what type of characteristic? Categorical variable Suppose that every day the proportion of all passengers on the GRTC Pulse that are either students or employees of VCU is determined. Based on this, the proportion of daily passengers on the GRTC Pulse who are either students or employees of VCU is what type of characteristic? Continuous Quantitative Variable For each GRTC Pulse, the number of stops it makes per day are counted. What type of characteristic is the number of stops for each GRTC Pulse? Discrete Quantitative variable Suppose a sample of 35 passengers who have ridden the GRTC Pulse since service was launched is selected, as follows. As they board, passengers are asked if they live in the City of Richmond, Henrico County, Chesterfield County, Hanover County, or another location (5 options). A random sample of 7 passengers who have ridden the GRTC Pulse since service was launched was randomly chosen from each of the 5 locations. What type of sampling procedure is this an example of? Stratified random sampling A sample of 300 passengers who have ridden the GRTC Pulse since service was launched was selected in the following manner. There are a total of 14 GRTC Pulse stations. A random sample of 5 of the 14 GRTC Pulse stations was selected. Then for each of these 5 GRTC Pulse stations (but not the other 9), a random sample of 60 passengers who boarded from that station was selected. What type of sampling procedure is this an example of? Multistage random sampling This is a concept/definition question: which of the following sampling methods would give the highest likelihood of getting a sample of GRTC Pulse passengers that is representative of all GRTC Pulse passengers in the population? Stratified random sampling On their website GRTC Pulse lists five different time periods: AM Peak (6:00-9:00 AM), Midday (9:00 AM - 4:00 PM), PM Peak (4:00 - 7:00 PM), Off Peak (7:00 - 11:30 PM), and Late Night (11:30 PM - 6:00 AM). Of interest is to determine which of these five time periods has the highest passenger satisfaction rating. Hence a study was conducted, as follows. A sample of 40 passengers from each time period was selected (40*5 = 200 total passengers), and as they exited the GRTC Pulse they were asked to complete a very short satisfaction survey. The survey results for the passengers in each group were averaged, then the five averages were compared to determine which time period had the highest passenger satisfaction rating. As described, is this an example of a controlled experiment or an observational study? Observational study With stratified random sampling you select at least one subject from every group, while in multistage random sampling you first select some groups and hence subjects are not selected form every group? True For all passengers who have ridden the GRTC Pulse since service was launched, of interest is to determine the mean age of all the passengers. Suppose a sample of 20 passengers who have ridden the GRTC Pulse since service was launched was selected. The sample is purposely selected such that all 20 passengers were employed by VCU; passengers employed by other agencies and companies are excluded from the sample. In this scenario, what type of bias could this cause? Selection bias The population of interest is all VCU employees and the parameter of interest is the proportion of all VCU employees who use the GRTC Pulse service. Suppose a sample of 100 VCU employees were randomly selected and contacted, but only 50 of them responded and answered the questions. If the characteristics of those who did respond and those who did not respond are different, what type of bias would this create? Nonresponse bias An Italian restaurant is interested in comparing a new method for preparing ravioli with the current method. They decide to conduct a study, as described below, to determine which method they will use. The study takes place over a two-week period and involves all customers who order raviolis during that time. With each order, a coin is flipped. If the coin lands on heads, the ravioli is prepared using the new method; if the coin lands on tails, the ravioli is prepared using the current method. After the meal, the customers are given a short, anonymous questionnaire in which they are asked to rate the quality of the ravioli on a scale of 1 to 10 (with larger numbers reflecting higher satisfaction). At the end of two weeks the data are analyzed and the results compared. As described, is this an example of a controlled experiment or an observational study? Controlled experiment An Italian restaurant is interested in comparing a new method for preparing ravioli with the current method. They decide to conduct a study, as described below, to determine which method they will use. The study takes place over a two-week period and involves all customers who order raviolis during that time. With each order, a coin is flipped. If the coin lands on heads, the ravioli is prepared using the new method; if the coin lands on tails, the ravioli is prepared using the current method. After the meal, the customers are given a short, anonymous questionnaire in which they are asked to rate the quality of the ravioli on a scale of 1 to 10 (with larger numbers reflecting higher satisfaction). At the end of two weeks the data are analyzed and the results compared. As described in the example what is the response variable? Rating of the quality of ravioli An Italian restaurant is interested in comparing a new method for preparing ravioli with the current method. They decide to conduct a study, as described below, to determine which method they will use. The study takes place over a two-week period and involves all customers who order raviolis during that time. With each order, a coin is flipped. If the coin lands on heads, the ravioli is prepared using the new method; if the coin lands on tails, the ravioli is prepared using the current method. After the meal, the customers are given a short, anonymous questionnaire in which they are asked to rate the quality of the ravioli on a scale of 1 to 10 (with larger numbers reflecting higher satisfaction). At the end of two weeks the data are analyzed and the results compared. As described in the example, what is the treatment? The method of preparing ravioli A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 66 35 22 44 32 37 Calculate the mean of the data. 48 A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 66 35 22 44 32 37 Calculate the median of the data. 45.5 Which of the following is a measure of center that would be heavily influenced by outliers? Mean What type of characteristic is "number of enrolled students in a class"? Discrete quantitative variable Which of the following is a measure of center that is resistant to outliers? Median A simple random sample of 16 classes being taught at VCU during the fall 2017 semester was selected and for each the number of enrolled students recorded. The data is given below. 66 35 22 44 32 37 Calculate the range of the data.