MATH 300 Statistics Introduction to Statistics Milestone 1

MATH 300 Statistics Introduction to Statistics Milestone 1 1 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' current and previous grades, then interviewing a random selection of students about their eating habits. 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 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 college and asking current undergraduates to report their grades and eating habits from high school. 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. 2 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 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 survey A single-blind study A double-blind study A census RATIONALE Since she asks people what their preferences would be, this is an example of a survey. 3 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? Voluntary response sampling Convenience sampling Stratified sampling Systematic 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. 4 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? Matched-Pair Design Completely Randomized Design Simple Random Design Randomized Block Design RATIONALE By matching on age and gender this is called a matched-pair design. 5 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 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. Jenae monitors the habits of the co-workers who do not drink coffee. 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. 6 A poll was conducted two weeks before an election and showed that the incumbent would win with 54% of the vote, with a 3% margin of error. What is the confidence interval for this poll? 54% - 3% 54% + 3% 48% to 60% 51% to 57% RATIONALE Recall for a confidence interval, we take the point estimate +/- margin of error. Using this framework we take the point estimate of 54%, then add and subtract the margin of error, 3%. l o w e r space b o u n d colon thin space 54 percent sign minus 3 percent sign equals 51 percent sign u p p e r space b o u n d colon thin space 54 percent sign plus 3 percent sign equals 57 percent sign This gives us a CI of 51% to 57%. 7 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 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 all the pizza shop's customers 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. 8 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 Non-response bias Deliberate bias Selection 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. 9 Which of the following data types will be continuous? The number of students who like chocolate or strawberry or vanilla ice-cream flavors The number of books in the school library The letter grade Tyron received on an English test The amount of snow that fell last night RATIONALE For data to be continuous, it must be able to take on any value inside of an interval. The amount of snow that falls can be any value and is therefore continuous. All the other measures can only take on a limited number of values. 10 Which of these random samples represents a representative sample of the number of students who enjoy science class? 30 students who failed science class last year 30 students who received high grades in their science class last semester 30 students in the lunchroom 30 students who participated in the science fair 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. 11 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 There is no bias in the way this survey is carried out. Selection bias 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. 12 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. 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 distributors who supply the products to local retailers about the popularity of different soup brands. Ask customers who visit retailers within a 15 mile radius of the company headquarters. Ask customers who visit the grocery store nearest to the manager's house which soup they like 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. Although asking retailers doesn't directly contact customers, by asking all retailers about their customers they will better capture customers in general than simply asking those who are near the company headquarters or those who live near the manager. 13 Several scientific and statistical studies have been done to determine whether or not pollutants in soil increase the incidence of cancer. A study based on many previous studies summarizes that there is no link between pollutants in soil and cancer. This kind of statistical study is called a __________. Clinical trial Prospective study Retrospective study Matched-pair design RATIONALE Since the data has already been collected it is called a retrospective study design. 14 In 2007, 4% of people buying new cell phones purchased a bluetooth earpiece during the same transaction. In 2012, 28% of people buying new cell phones purchased a bluetooth earpiece during the same transaction. Of the following choices, what is correct about the growth of bluetooth sales? It rose by 12%. It rose by 120 percentage points. It rose by 24%. It rose by 24 percentage points. RATIONALE We can note that the absolute difference between 2007 and 2012 is 4% to 28% or 24 percentage points. So we can say that sales actually grew 600%. 15 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 within city limits complete the survey. 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 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. 16 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 control group a treatment group the placebo effect a case-control study 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. 17 You skipped this question and it was marked incorrect. An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2,534 residents. It asks a group of 85 randomly selected people in the town about their age. Select the statement that is TRUE. None of the answer choices are true. The sample is 85 people. The population is 2,449 people. The sample is 85 people. The population is 2,534 people. The sample is 2,534 people. The population is 85 people. 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 2534 residents, with the sample being the 85 that were chosen to be analyzed about their age. 18 You skipped this question and it was marked incorrect. 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% -4.0% -4.2% 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: a b s o l u t e e r r o r equals o b s e r v e d minus a c t u a l equals 125 minus 120 equals 5 ==4.2% 19 A local gym conducts a survey among the people in a mall. Which survey question would have a qualitative response? How many servings of fruits do you eat every day? How much do you weigh, in pounds? Do you exercise daily? What is the amount of weight you can bench press, in pounds? RATIONALE Simply stating yes or no is simply descriptive and cannot be measured numerically or used in arithmetic, so it is qualitative. 20 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 Randomized Block Design Representative Sample 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. 21 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? Cluster sampling Systematic random sampling Multi-stage 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. 22 “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? Closed and binomial question Open question Open 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. 23 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 High accuracy and low precision Low accuracy and high 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. 24 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 $189.7 in 2004 $100 in 2004 would have been worth 189.70 in 1983. $100 in 2002 would be equivalent to $189.70 in 2004 $100 in 1983 would be equivalent to $189.70 in 2004 RATIONALE Recall that the CPI allows us to transform values from some year to values in another year. The value of the CPI in the base year is 100. Since the CPI in 2004 is 189.7, this means that for $100 in the base year of 1983 is equivalent to $189.7 in 2004. 25 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 Case-Control Design Completely Randomized Design Matched-Pair Design RATIONALE Since women are randomly assigned chocolate or placebo, this is a completely randomized design. 26 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) ________. matched-pair designed experiment randomized experiment blind experiment completely 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. 27 The blood bank at a hospital has 1,200 units of blood, out of which 37% units are of blood group B+. A clinical researcher randomly selects 300 units of blood and finds that 33% of those are of blood group B+. To test his result, he randomly selects 200 units of blood and finds that 40% of those are of blood group B+. Which of the following is the reason there is a difference between the two percentages selected by the researcher? Random error; the numbers were different due to variability inherent in sampling. The samples were not random samples. Both samples suffered from non-response bias. The sample sizes were both too small. RATIONALE When sampling, there is always some variability that occurs. So, although the sample values are different, since they were randomly chosen, the differences are simply due to the variability that comes from sampling and not due to some systematic bias. 28 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? Time spent studying Time spent using a cell phone Grade earned during the spring semester Grade earned during the fall semester 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. 29 Select the correct statement regarding experiments. A researcher can carefully control the explanatory variables and observe human responses. A researcher can carefully control the explanatory variables but not observe human responses. A researcher can observe the explanatory variables but not control human responses. A researcher can ignore explanatory variables and observe 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.