## Exam (elaborations)

# MATH 1280 Milestone 1_Introduction to Statistics (2020) – University of the People | MATH1280 Milestone 1_Introduction to Statistics (2020)

1 MATH 1280 Milestone 1_Introduction to Statistics (2020) – University of the People The administrator of a hospital conducted a survey among patients in the cardiology wing to determine service levels of the nursing staff in the hospital. Which of the following explains how the results of the survey could be biased? • The sample does not include the doctors of the hospital. • The sample does not include all the patients in the hospital. • The sample does not include the board members of the hospital. • The sample does not include the staff members of the hospital. RATIONALE Since the patients asked are only from the cardiology unit, it might not represent patients in all sections of the hospital. It would be better to include all areas of the hospital. CONCEPT Bias 2 The following shows the Consumer Price Index (CPI) for the years 2000-2005. All of the values use a reference year of 1983. Which of the following is true about the CPI, based on the information? • $100 in 2000 would be equivalent to $183.70 in 2003. • $100 in 2001 would have been worth 189.70 in 1983. • $100 in 1983 would be equivalent to $172.40 in 2000. • $100 in 2005 would be equivalent to $194.50 in 1983. RATIONALE Recall the CPI gives us a measure of price changes over time and allows us to transform values in one year to another. The value of the CPI in the base year is 100. This means that for $100 in 1983 is equivalent to$172.4 in 2000. CONCEPT Index Number and Reference Value 3 Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly. Select one control in Jenae's experimental study. • Jenae monitors the habits of the co-workers who do not drink coffee. • Jenae uses different locations in the kitchen for the coffee pots. • Jenae places condiments at random places throughout the kitchen. • Jenae makes sure that the coffee in different pots is brewed at the same time. RATIONALE In an experiment, controls are when conditions are manipulated by the experimenter to keep conditions as consistent as possible. In this example Jenae brews coffee at the same time, so this is a control. CONCEPT Experimental Design 4 In a survey of small business owners, a response to which of the following questions would be qualitative? • How many businesses do you own? • What type of business do you own? • How long have you owned a business? • How much did your business have in profits last year? RATIONALE All the other options are numeric measures and can be used in arithmetic. The type of business you have is simply a descriptive measure and is therefore qualitative. CONCEPT Qualitative and Quantitative Data 5 At a school of 900 students, 20% have blue eyes. A student randomly selects 100 students and finds 17% of them have blue eyes. A second student takes another random sample of 90 students and finds 24% of them have blue eyes. Which of the following explains why there is a difference between the two percentages? • The samples were not random samples. • Both samples suffered from non-response bias. • Random error; the numbers were different due to variability inherent in sampling. • The sample sizes were both too small. RATIONALE When sampling, there is always some variability that occurs. So, although the sample values are different and not equal to the true overall proportion of 20%, since they were randomly chosen, the differences are simply due to the variability that comes from sampling and not due to some systematic bias. As the sample size increases we would expect these differences to get smaller. CONCEPT Random and Systematic Errors 6 A travel agency contacted a department store and obtained the list of all people who made purchases using their credit cards at the store in the last month. The agency then surveyed a random sample from the list, calling them to ask their preference for air travel or train travel for taking holidays. Which of the following types of bias affects the conclusions of the survey? • Response bias • Deliberate bias • Selection bias • Non-response bias RATIONALE Selection bias is when the mode of selection introduces a bias in the sample so that it is not representative of the population of interest. Since they only collected information from those using their credit card at a department store, this does not represent how people travel in general and is therefore an example of selection bias. CONCEPT Selection and Deliberate Bias 7 Which of the following data types will be continuous? • Cost of a can of tuna fish • Number of people in a family • Height of a toddler • Number of chairs in a house RATIONALE The height of a toddler can take on any value, while the other measures can only be a limited number of values. So, the height of a toddler is continuous. CONCEPT Discrete vs. Continuous Data 8 Mike wants to find out the approximate income for professors in Michigan. He decides to randomly select 50 professors who work for a college or university in Michigan and obtain their salaries. What are the sample and the population of Mike's study? • The 50 professors that Mike interviews are his sample, and the professors that Mike does not interview are the population. • The 50 professors that Mike interviews are his sample, and all of the professors who work in Michigan are the population. • All of the professors who work in Michigan are the sample, and the 50 professors that Mike interviews are the population. • The professors in Michigan are the sample, and all the professors in the United States are the population. RATIONALE Recall the entire set of interest is the population and a sample is a subset of that population. In this question the entire set are all the professors at a university or college in Michigan, with the sample being the 50 that were chosen to be analyzed about their salary. CONCEPT Sampling 9 A survey result shows that cell phone usage among teenagers rose from 63% in 2006 to 71% in 2008. Of the following choices, which statement about cell phone use among teenagers is true? • Cell phone usage rose by 12.7 percentage points. • Cell phone usage rose by 8%. • Cell phone usage rose by 11.2 percentage points. • Cell phone usage rose by 12.7%. RATIONALE We can note that the absolute difference between 2006 and 2008 is 63% to 71% or 8 percentage points. To get the percent difference we take the absolute difference and divide by the initial value: So we can say cell phone usage rose by 12.7%. CONCEPT Using Percentages in Statistics 10 Scientists want to test a new pair of running shoes. A speed test is performed with two separate groups of participants. The treatment group will wear the new pair of running shoes, while the control group will not. It is believed that age and height may affect speed. Which of the following would be most effective in controlling the confounding variables, such as age and height, in this study? • A longitudinal observational study • A matched-pair design experiment • A completely randomized design experiment • A retrospective observational study RATIONALE In order to control for variables that may affect the study, a matched pair design which matches as closely as possible for those variables would best control for their effects. CONCEPT Matched-Pair Design 11 James participated in an archery competition. He was allowed four attempts and was supposed to hit the bullseye in the center of the board. If the figure shows the positions of James' arrows, which of the following would best classify the arrangement of arrows? • High accuracy and high precision • Low accuracy and high precision • High accuracy and low precision • Low accuracy and low precision RATIONALE The arrows are close to the center so they are accurate and they are also close to one another, so they are precise as well. CONCEPT Accuracy and Precision in Measurements 12 James conducts a survey to study the relationship between cell phone use and grades earned during the fall semester. James suspects that there might be a lot of other factors that affect grades besides cell phones. Which of the following could be a confounding variable in James's study? • Grade earned during the spring semester • Grade earned during the fall semester • Time spent studying • Time spent using a cell phone RATIONALE Recall a confounding variable is related to the outcome and explanatory variable and is not accounted for in a study. Although cell phone usage may be related to grades, by not accounting for study time, which is most likely related to grades, it confounds the results between cell phone usage and grades. So we can say study time is a confounding variable. CONCEPT Variables 13 To test the effectiveness of a new, cholesterol-lowering drug, a group of researchers recruits 200 volunteers with high cholesterol to take part in a study. The researchers place the numbers 1 through 200 in a hat and have each participant select a number. Those who picked an odd number receive the new drug, while those who picked an even number receive a placebo. Which experimental design are the researchers using? • Matched-Pair Design • Representative Sample Design • Randomized Block Design • Completely Randomized Design RATIONALE When all patients are assigned treatment or control randomly without considering other factors, this is called a completely randomized design. CONCEPT Completely Randomized Design 14 To compare the teaching methodologies of two of its eighth-grade math teachers, a school decides to compare student test scores from the two classes throughout the year. Which type of statistical study is the school conducting? • Meta-analysis • Prospective observational study • Retrospective observational study • Matched-pair design study RATIONALE A study which gathers data moving forward is called a prospective study. Since the data is gathered on students without controlling the setting moving forward, it is a prospective observational design. CONCEPT Prospective and Retrospective Studies 15 Which of these random samples represents a representative sample of the number of students who enjoy science class? • 30 students in the lunchroom • 30 students who participated in the science fair • 30 students who received high grades in their science class last semester • 30 students who failed science class last year RATIONALE For a sample to be representative it needs to look like the entire set of interest. By choosing students in the lunchroom, they are drawing upon all students in the school and not an unrepresentative one. CONCEPT Random & Probability Sampling 16 A research team conducts a survey to determine the area of land used for farming in Iowa. The team randomly selects house addresses and sends the survey by mail. Which type of sampling method is the research team using? • Systematic random sampling • Multi-stage sampling • Cluster sampling • Simple random sampling RATIONALE By choosing randomly from the house addresses all households should have an equal chance of being chosen. This would make it a simple random sample. CONCEPT Simple Random and Systematic Random Sampling 17 In a bolt-manufacturing factory, it is estimated that 6% of the bolts being manufactured will be defective, with a 3% margin of error. Choose the statement that correctly describes the confidence interval. • The percentage of defective bolts is between 3% and 6%. • The percentage of defective bolts is 6% or less. • The percentage of defective bolts is between 3% and 9%. • The percentage of defective bolts is 6% or more. RATIONALE Recall for a confidence interval, we take the point estimate /- margin of error. Using this framework we take the point estimate of 6%, then add and subtract the margin of error, 3%. This gives us a CI of 3% to 9%. CONCEPT Margin of Error 18 Jessica uses a poorly calibrated stopwatch to note the finish time of a relay race. She noted the time as 125 seconds, whereas the actual time taken was 120 seconds. The percent error in Jessica's calculation is __________. • -4.2% • 4.2% • 4.0% • -4.0% RATIONALE Recall that the percent error is equivalent to the absolute difference divided by the actual value. If the actual measure is 120 seconds and the observed measure is 125 seconds, then the absolute difference is: So we calculate the percentage error to be: CONCEPT Absolute Change and Relative Change 19 Select the correct statement regarding experiments. • A researcher cannot control the environment but can observe the response. • A researcher can control the environment but cannot observe the response. • A researcher can control the environment and observe the response. • A researcher can neither control the environment nor observe the response. RATIONALE The defining part of experimental setting is that the researcher can control the setting and apply some treatment to observe how it affects an outcome of interest. CONCEPT Observational Studies and Experiments 20 A researcher would like to determine which age groups (18-29, 30-49, 50-64, 65 or older) in the United States currently identify playing golf as their favorite pastime. Which statistical study would be most appropriate to answer this question? • A prospective observational study • A census • A single-blind experiment • A survey RATIONALE In order to obtain information about favorite pastimes, it would be best to solicit information from people directly by using a survey. CONCEPT Surveys 21 A scientist is conducting a study on the effect of eating chocolate and overall mood. They believe that gender is a significant factor. The participants are divided by gender. Then, within each group, participants are randomly assigned to consume either chocolate or a placebo and then rate their mood for the day. This experiment will run for two weeks. Which type of experimental design does this situation describe? • Case-Control Design • Matched-Pair Design • Completely Randomized Design • Randomized Block Design RATIONALE Since women are randomly assigned chocolate or placebo, this is a completely randomized design. CONCEPT Randomized Block Design 22 A grocery store owner asked the first 20 children who visited the store one day about their favorite snack. This is what type of sampling? • Systematic sampling • Convenience sampling • Voluntary response sampling • Stratified sampling RATIONALE Recall that convenience samples are samples taken due to their ease of gathering information. Since he simply asked the first 20 children, this is an example of that. Convenience samples are generally biased as they probably don't represent the entire set of interest. CONCEPT Convenience & Self-Selected Samples 23 A pizza owner asked 50 customers to taste a new type of topping and found that 40 people liked its taste. Which of these is an example of descriptive statistics? • 80% of the surveyed customers like the taste of the pizza topping. • 80% of all the pizza shop's customers like the taste of the pizza topping. • 80% of all people like the taste of the pizza topping. • 80% of the people in the city where the pizza shop is located like the taste of the pizza topping. RATIONALE Recall a descriptive statistic is a summary figure which uses the sample information at hand. Using the sample information we know 40 of 50 people or 80% like the taste of the pizza topping. CONCEPT Statistics Overview 24 The owner of a new store on Main Street wants to turn the boulevard outside into extra parking spaces because she is concerned about parking availability. She randomly selects 500 residents of the town to take a survey, and these individuals have confirmed their participation. One of the survey questions reads, “Many residents believe the lack of available parking on Main Street is a major problem, and extra spaces along the boulevard would help. Do you agree?" The store owner's survey could suffer from which type of bias? • Nonresponse bias • There is no evidence of bias in the way this survey is carried out. • Response bias • Selection bias RATIONALE By stating that many residents already believe parking is an issue and putting a response inside of the question, this is a good example of response bias. CONCEPT Nonresponse and Response Bias 25 Jay wants to study nutrition and performance in schools using available data. Which of the scenarios below will provide Jay with available data? • Going to a local high school and asking the principal for information about students' previous grades, then interviewing a random selection of students about their eating habits. • Going to a local college and asking current undergraduates to report their grades and eating habits from high school. • Going to a local high school and asking the principal for information about students' current and previous grades, then asking the health teacher for the results from a survey students took in health class. • Going to a local high school and asking the principal for information about students' current and previous grades, then interviewing a random selection of students about their eating habits. RATIONALE Recall, for data to be considered available data it must already be collected. Since the grades data and survey data were already collected these are examples of available data. CONCEPT Data 26 Melissa is conducting a survey of her classmates because her teacher wants the class to learn more about hygiene habits. Melissa has developed a list of 10 questions. “Do you brush your teeth every day?” is the first question she asks. Which type of question is Melissa asking? • Open question • Closed question • Open and binomial question • Closed and binomial question RATIONALE In this question, the responses are limited and there are only 2 responses. This would be a closed binomial question type. CONCEPT Question Types 27 The city government wants to conduct a survey on the number and types of cars owned by its residents. How can the city use the cluster sampling method to find this information? • The city has every household in 10 neighborhoods complete the survey. • The city selects only those households that have more than one vehicle to complete the survey. • The city has every household within city limits complete the survey. • The city selects 100 households at random to complete the survey. RATIONALE Recall that clusters are generally geographic groups. So, the city can put the neighborhoods into clusters and then choose a random sample of those clusters. CONCEPT Stratified Random and Cluster Sampling 28 Jenae is able to purchase a different brand of coffee for half the price from a new supplier. She anticipated that her co-workers would object to switching to the new brand, as they were really partial to the coffee they have been drinking so far. Indeed, when offered a taste test of the old brand versus the new brand, her co-workers unanimously rejected the new brand. Jenae's boss, Steven, pointed out that this result was most likely due to the fact that the taste test was not ________. • controlled • blinded • replicated • randomized RATIONALE Since they didn't keep the participants unaware of what brand they were tasting, this could influence the findings. So, the rejection of the new brand was likely due to not blinding them from what brand they were drinking. CONCEPT Blinding 29 Aaron has designed a trial to test a new energy drink. Fifty individuals in the treatment group try the new energy drink every day for two weeks, and they describe a moderate increase in their energy levels. Fifty individuals in the control group drink sugar water every day for two weeks, and they describe a significant increase in their energy levels. What has Aaron observed? • A confounding variable • A sampling error • The margin of error • The placebo effect RATIONALE Since no treatment was given to these participants in the control group and they reported an effect, this is what we refer to as the placebo effect. CONCEPT Placebo