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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
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
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.
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
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
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.
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
