MATH 1280 Practice Milestone UNIT 1 Introduction to Statistics_2020 | Introduction to Statistics_Milestone UNIT 1 _ Graded A

MATH 1280 Practice Milestone UNIT 1 Introduction to Statistics (2020) – University of the People Which of the following data types will be continuous? • Number of cars produced by a car company in a year • Number of skyscrapers in a city • Number of correct answers on a ten-question true/false test • Weight of a baby whale RATIONALE For data to be continuous, it means it can take on any value inside of an interval. Since the weight of a baby whale can take on any numerical value inside of possible ranges of weights, it is continuous. CONCEPT Discrete vs. Continuous Data 2 Which of the following correctly identifies a sample with non-response bias? • A person becomes ashamed to answer a question regarding his or her past drug use• The wording of a question about politics causes the subject to misinterpret the meaning of the question • A person selected to be a part of the survey is unable to be contacted or refuses to participate • A telephone poll excludes individuals who do not have phones RATIONALE Non-response bias is simply when someone can't respond or refuses to do so. CONCEPT Nonresponse and Response Bias 3 One typical way to select a sample is to randomly pick phone numbers from a telephone book. Which of the following explains how the selection of the sample could be biased? • The sample does not represent those that cannot afford a telephone. • All of these choices would introduce a bias. • The sample does not represent those that chose not to have a telephone. • The sample does not represent those do not list their phone numbers. RATIONALE By choosing to use a telephone number, they would be excluding anyone who might not use a phone, doesn't want their number public, etc. By excluding these types of people,they would not capture all people in the population and if these groups would respond differently in a study, the study would be biased. CONCEPT Bias 4 Max conducted a clinical trial for a new vitamin supplement. He had two groups in his clinical trial. The control group was given a sugar pill, and the treatment group was given the new vitamin supplement. However, many of the participants in the control group reported improvements in their general health, similar to the treatment group. The ________ may describe the reason some participants from the control group reported health improvements. • response variable • placebo effect • confounding variable • treatment group RATIONALE When people in a control group indicate that there is some noticeable change, in this case an improvement in health, this is an example of what we call a placebo effect. CONCEPT Placebo 5 In a survey of a large high school class, responses to which two of the following questions will be qualitative? • What is your height in inches?• Are you male or female? • Are you right-handed or left-handed? • How many minutes do you spend working on homework on a typical weeknight? RATIONALE Qualitative simply describes things and can't be represented with numbers which can then be used in arithmetic. Gender simply describes someone. CONCEPT Qualitative and Quantitative Data 6 Which of the following describes cluster sampling? • Choose a sample in such a way that every nth person or item is included. • Choose a sample so that every member of the population has an equal chance of being selected for the sample. • First divide the population into groups, and then randomly pick individuals from each group, so that the sample is proportionate to the population. • Divide the population into groups, and then randomly select some groups. Choose all the members within the selected groups to be part of the sample. RATIONALE Cluster sampling is when the population is broken up into clusters, which are generally based on something like geography. You then randomly choose groups or clusters and members of those clusters are included in the sample. CONCEPTStratified Random and Cluster Sampling 7 A sample composed of people who are readily available or easily recruited is called a __________ sample. • random • convenience • cluster • self-selected RATIONALE When you choose a sample based on how easy it is to gather the data, this is referred to as a convenience sample. CONCEPT Convenience & Self-Selected Samples 8 A professional quarterback completed 66% of his passes in 2008 and 68% of his passes in 2009. Of the following choices, which of the following TWO are correct about the quarterback’s completion rate? • It rose by 3%. • It rose by two percentage points. • It rose by 2%.• It rose by three percentage points. RATIONALE We can note that the absolute difference between 2008 and 2009 is 66% to 68% or 2 percentage points. To get the percent difference we take the absolute difference and divide by the initial value: So we can say the quarterback's completion rate rose by 3%. CONCEPT Using Percentages in Statistics 9 At a school of 1,500 students, 20% are left-handed. A student randomly selects 200 students and obtains 22% left-handed students. A second student takes another random sample of 250 students and obtains 27% left-handed students. Which of the following should the difference between the percentages be attributed to? • The sample sizes were both too small, which is why they both obtained figures different than 20%. • Random error; the numbers were different due to variability inherent in sampling. • Both samples suffered from non-response bias. • The samples were not random samples.RATIONALE When sampling from the population, even when you gather a random sample, there is not a guarantee it will exactly equal the true population value. So, even in this case where the sample values are not exactly equal to 20%, since the samples are randomly drawn, this is probably simply due to the variability that occurs when sampling. This is simply random error. CONCEPT Random and Systematic Errors 10 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 $178 in 2001. • $100 in 2004 would be equivalent to $189.70 in 1983.• $100 in 1983 would be equivalent to $194.50 in 2005. • The CPI does not change very much from year to year. RATIONALE Recall that the CPI is a way to adjust for price level changes from year to year. The base value for the CPI is 100 and all values are in reference to that value. Each CPI value for a corresponding year tells us what the value of $100 in the base year is in the corresponding year. So, the value of $100 in 1983 is equivalent to having $194.50 in 2005. CONCEPT Index Number and Reference Value 11 The type of experimental design that first divides participants into homogeneous groups before randomly assigning treatments and controls is called a(n) __________. • matched-pair design • randomized block design • multi-stage sampling • completely randomized design RATIONALE When we first break up items into block and then assign treatment, this is called a randomized block design. CONCEPT Randomized Block Design12 Which of the following definitions corresponds with an observational study? • Controlling the environment and observing the response • Measuring variables of interest but not attempting to influence responses • Selecting a sample from the population of all individuals about which information is desired • Doing something intentionally to the individuals involved RATIONALE An observational study is one in which the researcher doesn't try and control for the setting. They simply gather data on the variables in the study. An experiment is when the researcher intentionally or actively controls for the setting in which the study takes place. CONCEPT Observational Studies and Experiments 13 A poll was conducted two weeks before an election and showed that the incumbent would win with 56% of the vote and a margin of error of 4%. If the incumbent needs to receive at least half the votes to win the election, can there be confidence in the incumbent’s victory? • Yes, because the lowest the incumbent could receive is 52% of the vote. • Yes, because the poll stated that the incumbent will win with 60% of the vote.• No, because she could receive as low as 4% of the vote. • None of the above RATIONALE Recall for a confidence interval, we take the point estimate +/- margin of error. Using this framework we take the point estimate of 56%, then add and subtract the margin of error, 4%. This gives us a CI of 52% to 56%. Since the lower value is greater than 50%, we are confident that the incumbent should earn at last 50% of the votes and win the election. CONCEPT Margin of Error 14 Jenae also noticed that some of the coffee labels were much more visually attractive than others. She replaced 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 a weeklong experiment. Which of the following statements about Jenae's actions is FALSE? • By ensuring that the labels look the same, Jenae is controlling the "visual appearance" variable. • Because all of her labels are the same, Jenae could replicate her experiment for other companies. •By making sure that the labels all look the same, Jenae is ignoring randomization in her experiment. RATIONALE This is a description of an experiment. Jenae is controlling for things by using the same labels. This allows for replication in other settings. By doing this, randomization is not compromised. CONCEPT -- - - - - - -- Continued