STAT MISC Milestone 1-Completed and Graded A

STAT MISC Milestone 1 1 Sam counts how many people came to the local political meeting. He counts 72 people, but forgot about the 4 people sitting behind him. The percent error in his calculation is __________. • 50% • -5.3% • 5.6% • -2.8% RATIONALE Recall that the percent error is equivalent to the absolute difference divided by the actual value. If the actual number of people was 76, and the observed number of people was only 72, then the absolute error is: So we calculate the percentage error to be: CONCEPT Absolute Change and Relative Change 2 A sports trainer is going to do an experiment on the effect of Vitamin D supplements and his athletes. He randomly assigns all of his patients to either take Vitamin D supplements or take a placebo. What type of experimental design does this situation illustrate? • Completely Randomized • Matched-Pair • Simple Random • Randomized Block RATIONALE Since all athletes are assigned treatment or control for vitamin D randomly without considering other factors, this is called a completely randomized design. CONCEPT Completely Randomized Design 3 In a survey of small business owners, a response to which of the following questions would be qualitative? • How long have you owned a business? • How much did your business have in profits last year? • How many businesses do you own? • What type of business do you own? 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 4 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 9%. • The percentage of defective bolts is 6% or more. • The percentage of defective bolts is 6% or less. • The percentage of defective bolts is between 3% and 6%. 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 5 In a study to assess the risk of obesity with the amount of time exercised per week, researchers matched each patient, in a sample of 500 people who are obese, with a person of the same ethnicity, gender, and age (along with other similar characteristics) who is not obese. The researchers asked the patients and their matches a series of questions, and then tracked eating and exercise habits regularly for several years. Which type of statistical study are the researchers conducting? • Prospective study • Case-control study • Designed experiment • Retrospective study RATIONALE Since the study collected information on people over several years moving forward, it is a prospective study design. CONCEPT Prospective and Retrospective Studies 6 A trainer is studying the effects of vitamin D on his athletes. He has realized that there are many potential confounding factors, such as gender and age. To limit the effect of these confounding variables, he decided to first group two athletes together based on these variables (for example, two 21-year-old males). Then he randomly assigned one person to receive the vitamin D and the other to receive a sugar pill. What type of experimental design does this situation demonstrate? • Simple Random Design • Completely Randomized Design • Matched-Pair Design • Randomized Block Design RATIONALE By matching on age and gender this is called a matched-pair design. CONCEPT Matched-Pair Design 7 To determine what percentage of 376 teachers at a university were female, Ryan randomly selected 14 teachers. He then collected and analyzed his data. Select the statement that is TRUE. • There are 376 teachers in Ryan's sample, and 14 teachers are in the population. • There are 14 teachers in Ryan's sample, and 362 teachers in the population. • None of the answer choices are true. • There are 14 teachers in Ryan's sample, and 376 teachers are in 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 is the 376 teachers, with the sample being the 14 that were chosen to be analyzed. CONCEPT Sampling 8 Jenae's study ignored the fact that only some of her coffee choices had caffeine, even though her co-workers preferred caffeinated coffee. Therefore, Jenae decided to label one type of decaffeinated coffee as having caffeine to see what would happen. As she anticipated, this coffee became more popular with her co-workers, and they claimed that the extra boost of caffeine helped them focus on their work. The growing popularity of the decaffeinated coffee among co-workers, under the false impression that it gave them extra caffeine, is an example of ________. • a treatment group • the placebo effect • a case-control study • a control group RATIONALE Since no treatment of caffeine 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 9 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 ________. • blinded • replicated • randomized • controlled 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 10 A hunter is practicing his aim using a practice target. He takes 5 shots. All 5 shots hit the target, but they do not hit or surround the bullseye. In addition, all 5 shots are very spread apart on the target. Classify the hunter's accuracy and precision. • High accuracy and high precision • Low accuracy and high precision • Low accuracy and low precision • High accuracy and low precision RATIONALE Since the arrows fall away from the bullseye and are spread out we would classify this as low accuracy and low precision. CONCEPT Accuracy and Precision in Measurements 11 Which of these statements best defines a stratified random sample? • It is a sample where the population is divided into roughly equal groups, and then elements are randomly selected from each group. • It is a sample where the population is first broken into groups and then elements are randomly selected, in proportion, from each group. • It is a sample in which every element has the same chance of being selected from the total population. • It is a sample where every nth element of the population is selected in a sequence. RATIONALE Recall that a stratified random sample is first broken up into homogenous groups called strata. From those strata a random sample is then chosen. CONCEPT Stratified Random and Cluster Sampling 12 A retail brand plans to open its stores across all cities with a population of more than one million. To prepare for this, it refers to the past year's census done by the government. Which statement accurately describes the type of data the retail brand is using? • The census is an example of available data because the government provides it. • The retail brand is relying on available data because customers provide information to the census. • The census is an example of raw data because the government provides it. • The retail brand is relying on raw data because it has to ask for permission to use the census. RATIONALE Since the retailer doesn't gather the data itself, but relies upon data that has already been collected, this is an example of using available data. CONCEPT Data 13 Select the correct statement regarding experiments. • A researcher can carefully control the explanatory variables but not observe human responses. • A researcher can ignore explanatory variables and observe human responses. • A researcher can carefully control the explanatory variables and observe human responses. • A researcher can observe the explanatory variables but not control human responses. 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. The responses by the participants are not controlled by the researcher. CONCEPT Observational Studies and Experiments 14 Which of these random samples represents a representative sample of the systolic blood pressure of all patients in a hospital? • The systolic blood pressure of 50 patients in the neurology department. • The systolic blood pressure of 50 employees in the hospital. • The systolic blood pressure of 50 children admitted in the hospital. • The systolic blood pressure of 50 patients in the hospital. RATIONALE For a sample to be representative it needs to look like the entire set of interest. To look like all patients in the hospital, they should be randomly sampled from the entire population not simply the neurology department or children. Employees are not a part of the population of interest. CONCEPT Random & Probability Sampling 15 The traffic volumes at a major intersection in New York were surveyed every day between one and four in the afternoon for a month to study the traffic patterns in the city. Which of the following types of bias affects the conclusions of the survey? • Deliberate bias • Non-response bias • Selection bias • 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 1 to 4pm, this is a selection bias. CONCEPT Selection and Deliberate Bias 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? • Simple random sampling • Systematic random sampling • Multi-stage sampling • Cluster 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 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 staff members of the hospital. • 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. 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 18 A factory manufactures bolts. One of its employees, working in the quality control department, checks the first 20 bolts manufactured in a day for possible defects. This is what type of sampling? • Systematic sampling • Stratified sampling • Convenience sampling • Voluntary response sampling RATIONALE Recall that convenience samples are samples taken due to their ease of gathering information. Since they simply used the first 20 bolts, 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 19 The owner of a pizza parlor called every fifth person who ordered pizza last week to rate the pizza. What type of statistical study is this? • A survey • An experiment • An observational study • A census RATIONALE Since the owner asked patrons about the pizza and gathered information from them, this is an example of a survey. CONCEPT Surveys 20 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. • The sample sizes were both too small. • Random error; the numbers were different due to variability inherent in sampling. 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 21 A student group on a college campus wanted to create a survey about parking availability on campus. The student group randomly selected 300 students to take the survey. One of the questions read, “Many students believe the lack of available parking is a major problem. Do you agree or disagree?” Of the 300 students that took the survey, 285 surveys were returned. This survey will most likely suffer from which of the following types of bias? • Non-response bias • Selection bias • Response bias • There is no bias in the way this survey is carried out. RATIONALE By putting a response inside of the question which may lead survey participants to a given response, this is a good example of response bias. CONCEPT Nonresponse and Response Bias 22 Researchers want to test the effects of a new weight loss program. They believe that gender is a significant factor. The participants are divided by gender. Then, within each group, participants are randomly assigned to either the treatment or control group. Which of the following would be the most effective to test the effects of the new weight loss program? • A matched-pair design experiment • A completely randomized design experiment • A longitudinal observational study • A randomized block design experiment RATIONALE Since people are first put into gender and then are assigned treatment or control randomly this is called a randomized block design. CONCEPT Randomized Block Design 23 The following shows the Consumer Price Index (CPI) for the years . 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 $194.50 in 2005. • $100 in 2003 would be equivalent to $183.70 in 1983. • $100 in 1983 would be equivalent to $178 in 2001. • $100 in 2002 would have been worth $189.70 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 $178 in 2001. CONCEPT Index Number and Reference Value 24 A survey was conducted to find the frequency with which people go to the movies. A group of 120 people in a mall were asked about how often they go out for a movie and It was found that 36 people go to movies at least once in a month. Which of these is an example of descriptive statistics? • 30% of the people who visited the mall go to movies at least once in a month. • 30% of the people surveyed in the mall go to movies at least once in a month. • 30% of the people who reside in the county go to movies at least once in a month. • 30% of the people who reside in the city go to movies at least once in a month. RATIONALE Recall a descriptive statistic is a summary figure from a sample, which is the information at hand. From this survey a statistic would be 36 of 120 people or 30% go to the movies at least once in a month. CONCEPT Statistics Overview 25 Which of the following data types will be continuous? • The total weight of apples harvested in the farm in a season • The letter grades students received on a class quiz • The number of children younger than ten that visited a planetarium last week • The number of cars in 100 households RATIONALE The total weight of apples can take on any value and is therefore continuous. The other measures can only take on a limited number of values and are discrete. CONCEPT Discrete vs. Continuous Data 26 Jenae changed the original coffee labels with plain white ones that had the flavor printed in bold black letters, and she placed them on the coffee pots for the week-long experiment. Jenae used an aspect of experimental design known as ________ when she created the labels to have the same appearance. • randomization • a treatment • replication • a control RATIONALE In an experiment, controls are when conditions are manipulated by the experimenter to keep conditions as consistent as possible. When Jenae makes the labels the same the entire week, this is an example of a control. CONCEPT Experimental Design 27 An appliance store manager noted that the sales of home appliances contributed 74% of the store's profits in the year 2010 and 82% in the year 2011. Of the following choices, which statement about home appliance sales is true? • Home appliance sales increased profits by 8%. • Home appliance sales increased profits by 8 percentage points. • Home appliance sales increased profits by 9.75%. • Home appliance sales increased profits by 9.75 percentage points. RATIONALE We can note that the absolute difference between 2010 and 2011 is 74% to 82% or 8 percentage points. To get the percent difference we take the absolute difference and divide by the initial value: So we can say sales actually grew by 10.8%. CONCEPT Using Percentages in Statistics 28 Ben is measuring the effect that the potential energy of an object has on the height of an object's bounce. Which variable represents the height of an object's bounce? • Independent variable • Explanatory variable • Response variable • Confounding variable RATIONALE The outcome is the response, dependent or y -variable. This is the height or bounce in this example. CONCEPT Variables 29 It’s Saturday afternoon, and Denise is going shopping. She stops by a department store because she needs a new pair of shoes. She has picked out three styles that she likes. The store associate asks, “What is your shoe size?” Which type of question has the store associate asked? • Open question • Closed and binomial question • Closed question • Open and binomial question RATIONALE Recall a closed question has only a limited number of responses. Since she can only answer with her shoe size, this would be a closed question. CONCEPT Question Types