Question 1

A nutritionist wants to conduct a study to determine the efficacy of eating beans as an aid in weight loss. She randomly assigns half of a group of overweight persons to a treatment group who are given a planned diet which includes a variety of beans at two meals each day for six weeks. The other half of the group is given the same diet without the beans. Both diets are designed to have the same caloric content. A nurse at the nutrition center weighs each
Subject on Friday of each week. Select the potential source of confounding (if any).

Accepted Answer

The study is essentially free of confounding sources because the subjects are randomly assigned to treatment and control groups, and the diets are designed to have the same caloric content.

Question 2

Is the study experimental or observational
-Researchers at a medical school want to compare the rates of birth defects in babies born to mothers whose diets are classified as low fat with those born to mothers whose diets are high in fat. For one year, they collect data on all babies and their mothers in area hospitals, using information obtained from the mothers to determine whether they fall in the low fat or high fat diet category.

Accepted Answer

The study is observational because the researchers are not manipulating any variables or assigning mothers to specific diet groups; they are simply observing and collecting data based on existing conditions.

Question 3

A poll taken of 500 voters three months before the election showed that 55% favored the Republican candidate with a margin or error of 4%. A second poll of 500 voters taken two weeks later showed that 45% favored the Republican candidate, again with a margin of error of 4%. Consider the following possible explanations for these results.
"1) At least one of the polls is wrong since the ranges of possible values of the population
Parameter do not overlap."
2) Both polls are right, but voters changed their minds between the two polls.
"3) One of the polls selected a sample that was not representative of the population.
Which statements are possible explanations of the results?"

Accepted Answer

The results could be explained by voters changing their minds (statement 2) or by one of the polls having a non-representative sample (statement 3). The ranges of possible values do overlap when considering the margin of error, so statement 1 is incorrect.

Question 4

Is the study experimental or observational
-Researchers at a medical school want to compare two methods of treating blocked arteries. Fifty patients in similar condition are randomly assigned to two groups. One group is treated surgically and the other group is treated with drugs.

Accepted Answer

The study is experimental because the researchers are actively assigning treatments to the patients, rather than just observing them.

Question 5

Select the sample most representative of the population of interest in
-A researcher wishes to determine the average number of text messages per month sent by high school students who have cell phones.

Accepted Answer

Randomly selecting the cell phone records of 100 high school students would provide the most representative sample of the population of interest, as it would include all high school students with cell phones, regardless of whether they were seen talking on their phones or not.

Question 6

Determine whether the statement is based on sample data or census data
-In May of 2007, a Gallup poll asked the following question of 1007 people surveyed. Now thinking about how human beings came to exist on Earth, do you, personally, believe in evolution, or not? 68% of Republicans, 37% of Independents, and 40% of Democrats responded that they do not believe in evolution.

Accepted Answer

The data is based on a sample because it involves a survey of 1007 people, which is a subset of the entire population.

Question 7

Determine which evaluation guideline(s) apply in questioning the results of the described study
-A mathematics teacher wanted to determine whether assigning homework had a beneficial effect on student learning in first year algebra. His class met at 8:00 in the morning and he obtained the cooperation of another teacher of the same class that met at 2:00 in the afternoon.
He gave his class no homework while the other teacher continued to assign homework as he usually did. Both teachers gave the same tests so that they could compare the results.

Accepted Answer

All of the evaluation guidelines apply in questioning the results of the described study. The teacher did not consider possible confounding variables, such as the time of day the classes met. He also did not consider the sample, as the two classes may have been different in terms of their ability levels. Finally, he did not consider the measurement of the variable of interest, as the tests may not have been equivalent.

Question 8

A political science student randomly selects 100 names from the voter list of registered Democrats and 100 from the list of registered Republicans.

Accepted Answer

The student is using a stratified sampling method by dividing the population into subgroups (Democrats and Republicans) and then randomly selecting equal numbers from each subgroup.

Question 9

An internet supplier of refilled ink cartridges for ink jet printers sold cartridges to 30,000 customers over the past two months. A random sample of 1000 of those customers revealed that 180 were not happy with their purchase. The margin of error was 2%. What range is likely to contain the population parameter?

Accepted Answer

The sample proportion of unhappy customers is 18% (180 out of 1000). With a margin of error of 2%, the range for the population proportion is 16% to 20%.

Question 10

In a study of teen cell phone use, 117 high school students were observed as they drove out of their high school parking lot after school. Of these drivers, 46 were already talking on their cell phones as they drove out. What is the most probable purpose of this study?

Accepted Answer

The study observed high school students as they drove out of their high school parking lot after school, and counted the number of students who were already talking on their cell phones as they drove out. This suggests that the purpose of the study was to find out what percent of high school students use cell phones while driving.

Question 11

Determine whether the statement is based on sample data or census data
-The Centers for Disease Control and Prevention (CDC) reports that for the year 2003, 181,646 women and 1,826 men were diagnosed with breast cancer in the U.S.

Accepted Answer

The statement is based on census data because it reports the total number of cases diagnosed in the entire population of the U.S. for that year.

Question 12

Select the sample most representative of the population of interest in
-The state Department of Natural Resources is considering lowering the bag limit on Walleyed Pike on Mud Lake and wants to know how such a decrease will affect the number of people fishing on Mud Lake. Which of the following samples is most likely to provide the necessary information?

Accepted Answer

Interviewing all of the fishermen on the lake each Saturday in July is most representative because it directly targets the population of interest—those who are actively fishing on Mud Lake.

Question 13

A political campaign worker wishes to conduct a poll to determine how her candidate is likely to fare in the upcoming state Senate election. What is the population from which she should Choose her sample?

Accepted Answer

The population should include all citizens in the candidate's district who are likely to vote in the election, as they are the ones who will ultimately determine the election outcome.

Question 14

Determine whether the given value is a statistic or parameter
-A researcher interviewed a random sample of 100 library patrons as they were leaving the library and found that 54% of them had checked out books.

Accepted Answer

The value is a statistic because it is derived from a sample of the population, not the entire population itself.

Question 15

A researcher wanted to study the relationship between coffee drinking and heart problems. She interviewed all patients at several area hospitals and found that patients in the hospital for treatment of heart problems drank an average of 2.7 cups of coffee per day (Margin of error is 1.4 cups) while those patients being treated for other problems averaged only 1.4 cups of coffee per day (Margin of error is 0.8 cups). What conclusion can you draw about coffee as a
Cause of heart problems from this information?

Accepted Answer

The researcher only interviewed patients in hospitals, so the results may not be generalizable to the population as a whole.

Question 16

A quality improvement technician samples every $500 ^ { \text {th } }$ bag of potato chips coming off the assembly line to test the chips for fat content.

Accepted Answer

The technician is using a systematic sampling method by selecting every 500th bag in a sequence.

Question 17

Select the type of study most appropriate to the question
-Researchers at the University of Melbourne (Australia) wish to study the long-term effects of using repeated doses (instead of one dose) of antenatal corticosteroids to reduce the risk of respiratory distress syndrome in newborns. One of the factors to be studied is the body weight of the children at two years of age. What kind of study will best suit their purposes?

Accepted Answer

An experimental study is most appropriate as it allows researchers to control the administration of antenatal corticosteroids and directly observe the effects on the children's body weight at two years of age.

Quiz 1: Speaking of Statistics

Is the study experimental or observational -Researchers at a medical school want to compare two methods of treating blocked arteries. Fifty patients in similar condition are randomly assigned to two groups. One group is treated surgically and the other group is treated with drugs.

Select the sample most representative of the population of interest in -A researcher wishes to determine the average number of text messages per month sent by high school students who have cell phones.

A political science student randomly selects 100 names from the voter list of registered Democrats and 100 from the list of registered Republicans.

In a study of teen cell phone use, 117 high school students were observed as they drove out of their high school parking lot after school. Of these drivers, 46 were already talking on their cell phones as they drove out. What is the most probable purpose of this study?

Determine whether the statement is based on sample data or census data -The Centers for Disease Control and Prevention (CDC) reports that for the year 2003, 181,646 women and 1,826 men were diagnosed with breast cancer in the U.S.

A political campaign worker wishes to conduct a poll to determine how her candidate is likely to fare in the upcoming state Senate election. What is the population from which she should Choose her sample?

Determine whether the given value is a statistic or parameter -A researcher interviewed a random sample of 100 library patrons as they were leaving the library and found that 54% of them had checked out books.

A quality improvement technician samples every 500th 500 ^ { \text {th } }500th bag of potato chips coming off the assembly line to test the chips for fat content.

A quality improvement technician samples every $500 ^ { \text {th } }$ bag of potato chips coming off the assembly line to test the chips for fat content.