Exam 1: Collecting Data and Drawing Conclusions

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 sample in this study.

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 the two groups spend similar amounts on textbooks on average, but the amounts show much less consistency with humanities majors.

In a study reported in the September 24, 2007, issue of the Archives of Internal Medicine, German researchers described a study conducted on 1162 German adults suffering from chronic low-back pain. These subjects were randomly assigned to one of three groups: real acupuncture, sham acupuncture, and conventional therapy. Researchers found that $47 \%$ of subjects in the real acupuncture group improved, compared to $44 \%$ in the sham acupuncture group and $27 \%$ in the conventional therapy group. a. Identify the observational units in this study. b. Identify the explanatory variable. Also classify it as categorical or quantitative. If it is categorical, indicate whether it is binary. c. Identify the response variable. d. Is this an observational study or an experiment? Explain briefly. e. Did this study make use of random assignment or random sampling, or both, or neither? Explain briefly. f. Construct an appropriate graph to display the results. g. Comment on what the graph reveals. h. If the researchers find that the difference in improvement percentages between the real acupuncture group and the conventional therapy group is significant, would it be appropriate to conclude that real acupuncture causes a higher improvement rate than conventional therapy? Explain.

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. -Draw the appropriate graph to compare the responses of these two groups. Be sure to label the horizontal axis.

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 (in words) the parameters of interest in this study.

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 (in words) the statistic of interest.

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 quantitative variable described in this paragraph. (Be sure to state it as a variable.)

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. -Which would be an appropriate graph for comparing responses of these two groups - a dotplot or a bar graph? Explain why.

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 observational units in this study.

Suppose that the observational units in a study are the 23 campuses in the California State University system (e.g., Cal Poly, Long Beach State, Fresno State, Cal State Northridge, . . .). a. State a quantitative variable that you could record on these observational units. b. State a categorical variable that you could record on these observational units.

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. -Are the values listed $(\$ 26,984,43 \%)$ parameters or statistics? Explain.

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. -Would you consider the sample to be representative of the population, or is this sampling method biased? Explain. A national survey of 12- to 17 -year-olds conducted in 2011 found that teens who spend time on a social networking site in a typical day are three times more likely to use alcohol than teens who do not spend time on a social networking site in a typical day. Headlines proclaimed that social networking causes drinking. A blogger responded that this conclusion is not justified and that age is 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 -Which of these variables is 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. -Sketch what this graph would look like if it's not the case that all science majors spent more than all humanities majors, but there is a tendency for science majors to spend more than humanities majors on textbooks.

Classify each of the following statements as true or false: -Double-blind experiments are only necessary when the experimenters cannot be trusted to act ethically.

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. -Which would be appropriate for comparing responses of science and humanities majors - a dotplot or a bar graph? Explain why.

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. -For each group, calculate the proportion of patients whose warts disappeared completely.

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 sample and the sample size.

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 (in words) the parameter of interest.

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 concluding that eating dark chocolate causes a reduction in blood pressure? Explain briefly.