Unit1 Key Principles of Statistical Methods

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Southern New Hampshire University *

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Statistics

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Jan 9, 2024

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24/29 that's 83% RETAKE 24 questions were answered correctly . 5 questions were answered incorrectly . 1 Rachel, a professional bean bag athlete, throws three bean bags, aiming for the hole in the wooden board. However, her throws result in the bags spread out across the board as shown.

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Which of the following best classifies the arrangement of bean bags?  High accuracy and high precision  High accuracy and low precision  Low accuracy and low precision  Low accuracy and high precision RATIONALE The bean bags are not close to the hole and they are spread out. So they are not accurate or precise or we can say low accuracy and precision. CONCEPT Accuracy and Precision in Measurements Report an issue with this question 2 A poll conducted a week before the school election to the student council showed that Janice would win with 63% of the vote. The margin of error was 14%. If Janice needs to receive at least half the votes to win the election, can we be confident of Janice's victory?  No, because she could receive as low as 14% of the vote.  No, because she could receive as low as 49% of the vote.  Yes, because the poll stated that she will win with 63% of the vote.  Yes, because she could receive as much as 77% of the vote. RATIONALE Recall for a confidence interval, we take the point estimate +/- margin of error. Using this framework we take the point estimate of 63%, then add and subtract the margin of error, 14%.

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This gives us a CI of 49% to 77%. Given that you need to have at least 50% of the vote and we are confident that 49% is possible given our CI, we are not confident that Janice will win. CONCEPT Margin of Error Report an issue with this question 3 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 Report an issue with this question 4 The manager of a food company wants to conduct a survey to find out whether consumers like or dislike a new brand of soup that was recently launched.

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Which of the following data collection methods is mostly likely to get unbiased results?  Ask the employees in the company which soup is the best.  Ask customers who visit the grocery store nearest to the manager's house which soup they like the best.  Ask the sales team for the manufacturer which soup is best.  Ask customers from every region of the state which soup is the best. RATIONALE In order to get the best understanding of which soup is the most popular, they want to get a sense of what brands in general customers like. By asking customers from all around the state will better capture responses in general than simply asking those who are near the company headquarters or those who live near the manager. CONCEPT Bias Report an issue with this question 5 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 2003 would be equivalent to $183.70 in 1983.  $100 in 2002 would have been worth $189.70 in 1983.  $100 in 1983 would be equivalent to $178 in 2001.  $100 in 2000 would be equivalent to $194.50 in 2005. RATIONALE

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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 Report an issue with this question 6 On a candy production line, 3% of bags are overfilled. An employee randomly selects 100 bags and finds that 5% are overfilled. A second employees takes another random sample of 250 bags and finds that 2% are overfilled. Which of the following explains why there is a difference between the two percentages?  The samples were not random samples.  Random error; the numbers were different due to variability inherent in sampling.  The sample sizes were both too small, which is why they both obtained figures different than 3%  Both samples suffered from non-response bias. RATIONALE When sampling, there is always some variability that occurs. So, although the sample values are different from each other and the 3% true value, 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 would increase we would expect the variability to get smaller. CONCEPT Random and Systematic Errors Report an issue with this question 7 Which of the following data types will be continuous?

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 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  The total weight of apples harvested in the farm in a season 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 Report an issue with this question 8 A university wants to survey its undergraduates about their satisfaction with the new website. The university researchers pasted a link to the survey on the new website. A majority of the surveys showed that students were happy with the new website and found it easy to use. The university concluded that the website was fine and did not make any changes. However, on Friday, hundreds of students turned up at the Undergraduate Student Committee meeting complaining about how difficult it was to navigate the new website. University researchers realized that placing the survey on the website meant that people who liked the website were more likely to access the survey. Which of the following types of bias affected the survey's conclusions?  Non-response bias  Deliberate bias  Selection bias  Response bias

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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 who used the website, this does not represent how students in general feel about the website and is therefore an example of selection bias. CONCEPT Selection and Deliberate Bias Report an issue with this question 9 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?  Randomized Block Design  Completely Randomized Design  Matched-Pair Design  Case-Control Design RATIONALE Since people are first divided by gender and then are assigned chocolate or placebo randomly, this is called a randomized block design. CONCEPT Randomized Block Design Report an issue with this question 10

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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 fall semester  Grade earned during the spring semester  Time spent using a cell phone  Time spent studying 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 Report an issue with this question 11 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  Randomized Block Design  Completely Randomized Design

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 Matched-Pair Design RATIONALE By matching on age and gender this is called a matched-pair design. CONCEPT Matched-Pair Design Report an issue with this question 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 retail brand is relying on raw data because it has to ask for permission to use the census.  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. 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 Report an issue with this question 13 Which of these statements best defines a stratified random sample?

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 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 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.  It is a sample where the population is first broken into groups and then elements are randomly selected, in proportion, from each group. 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 Report an issue with this question 14 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 professors in Michigan are the sample, and all the professors in the United States 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 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. RATIONALE

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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 Report an issue with this question 15 A factory manufactures motorcycles. One of its employees, working in the quality control department, checks the first 10 and the last 10 motorcycles manufactured in a day. This is what type of sampling?  Systematic sampling  Voluntary response sampling  Convenience sampling  Stratified sampling RATIONALE Recall that convenience samples are samples taken due to their ease of gathering information. Since they simple used the first and last 10, 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 Report an issue with this question 16 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 hospital.  The systolic blood pressure of 50 employees in the hospital.

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 The systolic blood pressure of 50 patients in the neurology department.  The systolic blood pressure of 50 children admitted 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 Report an issue with this question 17 Select the correct statement regarding experiments.  A researcher can neither control the environment nor observe the response.  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. 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 Report an issue with this question 18 A survey result shows that cell phone usage among teenagers rose from 63% in 2006 to 71% in 2008.

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Of the following choices, which two statements about cell phone use among teenagers is true?  Cell phone usage rose by 8 percentage points. Cell phone usage rose by 11.2%.  Cell phone usage rose by 8 percentage points. Cell phone usage rose by 12.7%  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 Report an issue with this question 19 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?  Response bias

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 Selection bias  There is no bias in the way this survey is carried out.  Non-response bias 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 Report an issue with this question 20 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 water mixed with food coloring every day for two weeks, and they describe a significant increase in their energy levels. What has Aaron observed?  The margin of error  The placebo effect  A sampling error  A confounding variable 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 Report an issue with this question

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21 “Ugh,” Daniel says as he notices an office memo on his desk. It had been a fun weekend, and Monday morning came much too soon. He goes to the kitchen to refill his coffee mug. On the way, he runs into Sean, who asks, “How do you feel about the new office dress code?” Which type of question has Sean asked?  Open and binomial question  Open question  Closed and binomial question  Closed question RATIONALE In an open question, a responder can answer how they like. Since Sean can respond how he wants, this is an open question. CONCEPT Question Types Report an issue with this question 22 A new pet food product for small dogs has been developed to help with tooth decay. Fifty-two dogs participate in the study. Each dog owner picks a card from a standard deck out of a hat. If the card is red, their dog will be in the treatment group. If the card is black, their dog will be in the placebo group. Which experimental design was used?  Matched-Pair Design  Randomized Block Design  Completely Randomized Design  Case-Control Design RATIONALE

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Since all dogs are assigned treatment or control randomly by picking a card without considering other factors, this is called a completely randomized design. CONCEPT Completely Randomized Design Report an issue with this question 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 all the pizza shop's customers 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.  80% of all people like the taste of the pizza topping.  80% of the surveyed customers 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 Report an issue with this question 24 A local gym conducts a survey among the people in a mall. Which survey question would have a qualitative response?  Do you exercise daily?  How much do you weigh, in pounds?

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 What is the amount of weight you can bench press, in pounds?  How many servings of fruits do you eat every day? RATIONALE Simply stating yes or no is simply descriptive and cannot be measured numerically or used in arithmetic, so it is qualitative. CONCEPT Qualitative and Quantitative Data Report an issue with this question 25 A different coffee seller offered to sell coffee to Jenae's company for half the cost of their current brand. Jenae knew her co-workers were really partial to the coffee they drank now, so she decided to conduct a study to see if they noticed the difference in flavor. Her co-workers were convinced they would. Jenae provided each person with a sample and said that some had the new coffee and some did not. Only Jenae knew who had which brand of coffee. Jenae's strategy is an example of a(n) ________.  blind experiment  completely randomized experiment  matched-pair designed experiment  randomized experiment RATIONALE Since participants are unaware of what group they are in, regular or new coffee group, this is referred to as blinding in an experiment. CONCEPT Blinding Report an issue with this question 26

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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?  Retrospective observational study  Meta-analysis  Prospective 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 Report an issue with this question 27 Cindy measured and recorded the temperature of a liquid for an experiment. She used a poorly calibrated thermometer and noted the temperature as 100.5 degrees Fahrenheit. The actual temperature of the liquid was 95 degrees Fahrenheit. The percent error in her calculation is __________.  5.79%  4.08%  -5.79%  -4.08% RATIONALE Recall that the percent error is equivalent to the absolute difference divided by the actual value.

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If the absolute measure is 95 degrees and the observed measure is 100.5 degrees, then the absolute error is: So we calculate the percentage error to be: CONCEPT Absolute Change and Relative Change Report an issue with this question 28 Jenae brewed each coffee flavor using an identical coffee maker model, the same water source, and the same mass of ground coffee. Jenae used an aspect of experimental design known as ________ when she took these actions.  random assignment  replication  control  randomization RATIONALE In an experiment, control is the practice of keeping conditions as consistent as possible in order to avoid confounding variables. When Jenae makes the coffee in exactly the same way each day and for each flavor, she is practicing this principal of experimental design. CONCEPT Experimental Design Report an issue with this question 29 An art teacher is trying to determine which class to offer next summer. She passes out a slip of paper to some of the students in the class

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asking them whether or not they liked her course, and what class they would most like to see offered in the summer. Which type of statistical study is the art teacher conducting?  A census  A single-blind study  A survey  A double-blind study RATIONALE Since she asks people what their preferences would be, this is an example of a survey.

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Unit1 Key Principles of Statistical Methods

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