Exam 1: Collecting Data and Drawing Conclusions

Suppose an instructor wants to investigate whether statistics students who are taught using an online format learn just as much as students taught using a face-to-face format. a. Identify the explanatory variable in this study. b. Suggest a reasonable response variable for this study. c. Suppose students are given the option of signing up for their choice of the online or face-to-face format class. Then, if the online students perform significantly better than the face-to-face students, could the instructor reasonably conclude that the online format has beneficial effects? Explain the reasoning behind your answer.

Suppose you want to estimate the average waiting time at the coffee bar on campus. You decide to choose five days of the semester at random and then visit the coffee bar at four randomly chosen times on those days. You will record the waiting time for the customers who you find in line at those times and then calculate the average of these times. -Even though your sampling process involves multiple stages of randomness, it is still biased. Explain why and in which direction.

Consider the following dotplots of (hypothetical) ages for three groups of people: a. Which group tends to have the oldest ages? (No explanation or calculation is needed.) b. Which group tends to have the youngest ages? (No explanation or calculation is needed.) c. Which group has the most consistency in ages? (No explanation or calculation is needed.) d. Which group has the least consistency in ages? (No explanation or calculation is needed.)

Suppose the observational units in a study are customers arriving at a post office. For each of the following, identify whether it is a variable that can be recorded on these observational units. (No explanations are required; simply answer "yes" or "no.") a. Gender b. Total time spent waiting in line and being served c. Number of customers who arrive before noon d. Total amount of money spent e. Whether men or women spend more money on average

You want to compare prices of textbooks, so you ask six friends who are science majors and six friends who are humanities majors to report how much they spent on textbooks this term. -Sketch what this graph would look like if all science majors spent more than all humanities majors on textbooks.

You want to investigate whether teenagers in England tend to read more Harry Potter books than teenagers in the United States. -Identify the populations in this study.

Suppose you want to estimate the average waiting time at the coffee bar on campus. You decide to choose five days of the semester at random and then visit the coffee bar at four randomly chosen times on those days. You will record the waiting time for the customers who you find in line at those times and then calculate the average of these times. -Identify the population in this study.

a. Does taking a larger sample help to reduce the bias of a sampling method? Explain. b. Does taking a larger sample help to reduce the sampling variability of a sampling method? Explain.

Classify each of the following statements as true or false: -When subjects are randomly assigned in an experiment that compares a new treatment to a standard treatment, the subjects receiving the new treatment are guaranteed to perform better than subjects receiving the standard treatment.

You want to investigate whether teenagers in England tend to read more Harry Potter books than teenagers in the United States. -Identify the response variable, and classify it as categorical or quantitative. If you read a report that Hospital A has a higher mortality (death) rate than Hospital B when treating heart attack patients, it's possible that the severity of the patient's condition is a confounding variable.

An organization called The Knot Inc. hosts two popular wedding websites and conducted a national (U.S.) survey of nearly 19,000 couples who were married in the year 2010 . The organization reported that the average amount spent on a wedding, excluding honeymoon, was $\$ 26,984$ and that $43 \%$ of the ceremonies were held outdoors. -The press release describing this survey did not say how the 19,000 couples were selected. Explain why knowing this missing information is important.

An April 9, 2002, news release from the National Institutes of Health describes a study that investigated whether the herb St. John's wort is effective for treating depression. An excerpt from this press release follows: An extract of the herb St. John's wort was no more effective for treating major depression of moderate severity than placebo, according to research published in the April 10 issue of the Journal of the American Medical Association. The randomized, double-blind trial compared the use of a standardized extract of St. John's wort (Hypericum perforatum) to a placebo for treating major depression of moderate severity. The multi-site trial, involving 340 participants, also compared the FDA-approved antidepressant drug sertraline to placebo as a way to measure how sensitive the trial was to detecting antidepressant effects. a. Is this an experiment or an observational study? (Do not bother to explain.) b. Explain what it means for this study to be "double-blind" and also why this is an important component of the study design.

In a study reported in the July 6, 2007, issue of the journal Science, researchers studied 396 American college students and kept track of each student's gender and also how many words they spoke in a day. They found that women spoke an average of 16,215 words per day and men an average of 15,669 words per day. -Consider a new variable: whether the student spoke at least 10,000 words that day. Is this a legitimate variable to record in this study? Explain why or why not.

In a study reported in the July 6, 2007, issue of the journal Science, researchers studied 396 American college students and kept track of each student's gender and also how many words they spoke in a day. They found that women spoke an average of 16,215 words per day and men an average of 15,669 words per day. -Identify the categorical variable described in this paragraph. (Be sure to state it as a variable.)

In a recent study, researchers followed 104,000 U.S. veterans who had served in the armed forces and a comparison group of 216,000 nonveterans. Over a period of 12 years, they found that 197 veterans and 311 nonveterans committed suicide. a. Identify the explanatory and response variables in this study. Explanatory: Response: b. Is this an observational study or an experiment? Explain briefly. c. Calculate the proportion who committed suicide in the veterans group. Then do the same for the nonveterans group. Veterans group: Nonveterans group: d. The study also found that overweight people were much less likely to commit suicide than underweight people. Would you conclude that weight gain causes a lower risk of suicide? Explain briefly. e. Following the point about overweight people being less likely to commit suicide, the researchers said that smoking may be a confounding variable, however. Explain what this statement means in the context of this issue.

In a study published in the July 4, 2007, issue of the Journal of the American Medical Association, researchers investigated whether small doses of dark chocolate can reduce blood pressure for people who suffer from mild cases of high blood pressure. They recruited 44 German adults who were otherwise healthy except for mild cases of high blood pressure. These subjects were randomly assigned to either a dark chocolate group or a white chocolate group, and all subjects were instructed to eat one square portion of a chocolate bar (containing about 30 calories) every day for 18 weeks. They were also instructed not to eat any other cocoa products. Each subject had his/her blood pressure recorded at the beginning and end of the study, with the reduction in blood pressure calculated. It turned out that those in the dark chocolate group had an average reduction of about 3 points in systolic blood pressure, compared to a 0 point reduction on average in the white chocolate group. -Does the design of the study (the way the data were collected) allow for generalizing the results to the population of all people who suffer from a mild case of high blood pressure? Explain briefly.

Suppose for every email message that you receive in the next week, you keep track of - Whether the message is spam - Whether the sender is a family member, a friend, or someone else - Whether the message contains an emoticon (such as a smiley face ) - How many words are in the message - What day of the week the message was sent -What are the observational units in this study?

Studies conducted at elementary schools have shown that children with longer feet tend to score higher on reading tests than children with shorter feet. a. Are these studies observational or experimental? Explain briefly. b. Suggest a potential confounding variable that could explain the observed phenomenon that children with longer feet tend to score higher on reading tests than children with shorter feet. Describe what makes this a confounding variable.

Suppose for every email message that you receive in the next week, you keep track of - Whether the message is spam - Whether the sender is a family member, a friend, or someone else - Whether the message contains an emoticon (such as a smiley face ) - How many words are in the message - What day of the week the message was sent -State a research question that you could address with these data.

Consider the following dotplots of bowling scores for 15 games by three different bowlers: a. Which bowler tends to have the highest scores? (Do not provide explanations or calculations.) b. Which bowler tends to have the lowest scores? (Do not provide explanations or calculations.) c. Which bowler has the most consistency in his or her scores? (Do not provide explanations or calculations.) d. Which bowler has the least consistency in his or her scores? (Do not provide explanations or calculations.)