Exam 1: Collecting Data and Drawing Conclusions

Classify each of the following statements as true or false: -Random assignment tends to balance out variables that a researcher might not think about in advance, as well as variables that she does think about in advance.

Classify each of the following statements as true or false: -Random assignment guarantees that all variables will be perfectly balanced out between the treatment groups.

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. -Is the average that you calculate a parameter or a statistic? Explain.

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. -Identify the population of interest in this survey.

In the August 12, 2007, issue of Parade magazine (which comes with the Sunday newspaper for millions of Americans), readers were asked to go online and vote on the question: Should the drinking age be lowered? The results were published in the October 7 issue: More than 14,000 readers voted, and 48% said "yes." a. Is this number (48%) a parameter or a statistic? Explain (in one sentence or less) how you know. b. Do you trust this sample to be representative of the population of all American adults? Explain. c. How would you respond to someone who says, "Even if this had been a random sample, there's no way that a sample of 14,000 people could be representative of an entire country of 300 million people."

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 -Is people who send you a message with an emoticon a legitimate variable in this study? Explain why or why not.

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. -Identify the response variable in this study, and classify it as categorical or quantitative.

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. -What is the variable represented on the horizontal axis of these graphs? Be sure to label the horizontal axis (but you do not have to include a scale).

You want to investigate whether teenagers in England tend to read more Harry Potter books than teenagers in the United States. -Describe what it means for patient's condition to be a confounding variable in this context. Be sure to indicate how this potential confounding variable could be related both to the explanatory and the response variable.

On June 4-24, 2007, the Gallup Poll asked a nationwide sample of adult Americans about their attitude toward interracial marriage. Of the 2388 adults interviewed, $77 \%$ said that they approve of marriage between whites and blacks. a. Is this number $(77 \%)$ a parameter or a statistic? Explain briefly. b. What kind of graph would be appropriate for displaying the results of this survey - a dotplot or a bar graph? Explain briefly. (Do not create the graph.) c. Identify the sample size in this survey. d. How would you respond to a person who argued that this sample cannot possibly be representative of the population of all American adults, because there are more than 200 million American adults but fewer than 3000 in this sample?

Another article in the October 7, 2007, issue of Parade magazine claimed that one-third of all homicides in the United States remain unsolved. a. Is this number (one-third) a parameter or a statistic? (No explanation is needed.) b. What are the observational units? c. If a researcher studies a random sample of 150 homicides from around the United Sates, will he/she necessarily find that one-third of them remain unsolved? Explain briefly.

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. -Specify another variable that could have been recorded about the observational units in this study.

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 -How many of these variables are categorical? How many are binary?

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. -Is the number that you are trying to estimate a parameter or a statistic? Explain.

You want to investigate whether teenagers in England tend to read more Harry Potter books than teenagers in the United States. -Identify the explanatory variable, and classify it as categorical or quantitative.

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. -Identify the explanatory variable in this study, and classify it as categorical or quantitative.

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. -Is this an experiment or an observational study? Explain how you know.

A university wants to know the average yearly salary of its alumni ten years after graduation. It has a list of all alumni who graduated ten years ago and writes to each one, asking for information about annual salary. Suppose that $40 \%$ of the alumni respond to this invitation. -Describe what it means for age to be a confounding variable in this context. Be sure to indicate how this potential confounding variable could be related both to the explanatory and the response variables.

In a study reported in the Archives of Pediatric and Adolescent Medicine in October 2002 on treating warts, researchers investigated whether liquid nitrogen cryotherapy ("burning it off") or common duct tape would be a more effective treatment for kids with warts. The researchers found that 22 of 26 patients treated with duct tape saw complete disappearance of their warts, compared to 15 of 25 patients in the cryotherapy group. -Comment on what the graph reveals about the comparative effectiveness of these two treatments.

Classify each of the following statements as true or false: -Random assignment is not applicable for experiments with several treatment groups to be compared.