Lessons 11-17

Lesson 12- Discuss differences between following​ ?;s, each of which could be basis for statistical study. What % of Internet dates lead to​ marriage? What % of marriages begin w/Internet​ dates?

- ?'s have different populations.

Lesson 13- Describe importance of labeling on graph, &briefly discuss kinds of labels that should be included on graphs.

- Graph should have title or caption​ (or both) that explains what is shown​ &, if​ applicable, lists source of data. Without this​ label, might not be clear what graph is supposed to illustrate. - If multiple data sets displayed on single​ graph, there should be legend/key to identify individual data sets.​ Otherwise, comparisons among data sets not possible & confusion among data sets could occur. - Categories should be clearly indicated along horizontal​ axis, & there should be label that describes variable that categories represent. Without either, not possible to know what data graph is supposed to show. - #'s along vertical axis should clearly indicate scale, & there should be label that describes variable shown on vertical axis. Without either, would be no way of interpreting data shown in graph.

Lesson 13- What two types of graphs are most common when the categories are qualitative​ data?

- In bar​ graph, categories are clearly indicated along horizontal axis. Over each category is rectangle whose height indicates frequency or relative frequency of category. #'s along vertical axis clearly indicate the scale. - In pie​ chart, each category corresponds to wedge of circle. The size of each wedge is proportional to relative frequency of category it represents.

Lesson 12- Y/N: A research group that tracks tuition rates at colleges & universities compares the tuition at a small college today & 10 years ago & claims that tuition has increased​ 150% during that period.

- No, since it is not clear whether inflation was taken into account.

Lesson 13- What is distinction between qualitative data & quantitative​ data?

- Qualitative data describe​ categories, while quantitative data represent counts or measures. Brand names of shoes in consumer survey & eye colors are examples of qualitative data. Heights of students & quiz scores are examples of quantitative data.

Lesson 12- T/F: My experiment proved beyond a doubt that vitamin C can reduce severity of​ colds, bc I controlled experiment carefully for every possible confounding variable.

- Statement does not make sense bc inot always easy to discover confounding variables.

Lesson 13- Y/N: Your pie chart must be​ wrong, bc when I added the percentages on wedges, they totaled​ 124%.

- T: Statement makes sense bc pie charts are used primarily for relative​ frequencies, so total pie must always represent total relative frequency of​ 100%.

Lesson 13- Determine whether following variable is qualitative or​ quantitative & explain why. The annual salaries of NBA basketball players

- Variable is quantitative bc salaries are numerical categories.

Lesson 12- T/F: The local Chamber of Commerce claims that the average number of employees among all businesses in town is 12.5.

- ​No, there is not reason. The Chamber of Commerce would have no reason to distort its data.

Lesson 11- A researcher wants to determine the average. Describe how the researcher should apply the five basic steps in a statistical study.​ (Assume that all the people in the poll answered​ truthfully.) *The average number of workplaces per city that have a water cooler*

1. First basic step. - The population is all cities. The researcher wants to estimate the avg # of workplaces per city that have a water cooler. 2. Second basic step. - The researcher should gather data about water coolers from the largest sample of workplaces about whom the researcher can gather data. 3. Third basic step. - Sample statistic of interest is the avg # of workplaces per city that have a water cooler. 4. Fourth basic step. - Researcher should use the sample statistic as an estimate for the population value of the avg # of workplaces that have a water cooler & then uses the methods of statistics to determine how good that estimate is. 5. Fifth basic step. - Researcher should use the methods of statistics to determine the quality of the estimate of the population parameter & draw conclusions based on this estimate accordingly.

Lesson 11- A researcher wants to determine the average given below. Describe how the researcher should apply the five basic steps in a statistical study.​ (Assume that all the people in the poll answered​ truthfully.) The average time to failure of batteries in a particular model of stopwatch.

1. First basic step. - The population is all stopwatches of this model. 2. Second basic step. - Researcher should gather raw data about battery life from the largest sample of stopwatches about which he/she can gather data. 3. Third basic step. - Sample statistic of interest is the avg time for stopwatches in the sample to have their batteries wear down. 4. Fourth basic step. - Researcher should use the sample statistic as an estimate for the population value of the avg life of batteries & then use the methods of statistics to determine how good that estimate is. 5. Fifth basic step. - Researcher should use the methods of statistics to determine the quality of the estimate of the population parameter & draw conclusions based on this estimate accordingly.

Lesson 11- Study done at Center for Disease at certain university tracked 18,771 asymptomatic patients w/ certain disease who started therapy at different points in progression of infection. It was discovered asymptomatic patients who postponed antiretroviral treatment until disease more advanced faced higher risk of dying than those who initiated drug treatment earlier.

1. Identify population & population​ parameter(s) of interest. - Population is all asymptomatic patients w/ disease who have undergone treatment. Population parameters are survival rates & times which treatment began. 2. Describe sample & sample statistic. - Sample is 18,771 asymptomatic patients w/disease. Sample statistics are survival rates & times which treatment began for those in sample. 3. Identify type of study. - Observational study.

Lesson 11- In order to gauge public opinion about how to handle​ Iran's growing nuclear​ program, a research group surveyed 996 Americans by telephone and asked them to rate the threat​ Iran's nuclear program poses to the world on a scale of 1 to 10. Describe the​ population, sample, population​ parameters, and sample statistics.

1. Identify the population. - All Americans. 2. Identify the sample. - The 996 Americans surveyed by telephone. 3. Identify the population parameter. - The mean threat rating of all Americans on​ Iran's nuclear program 4. Identify the sample statistic. - The mean threat rating on​ Iran's nuclear program of the 996 Americans surveyed by telephone.

Lesson 11- Each​ year, a group surveys​ 50,000 households to study internet usage. In one area of the​ study, the group is interested in finding out how many hours a day the household spends streaming video from the internet. Describe the five basic steps in a statistical study.

1. State the goal of your study. In this​ case, it is to discover how many hours per day a household spends streaming internet video. 2.Choose a representative sample from the population. In this​ case, it would be choosing a sample of​ 50,000 households. 3. Collect raw data from the sample and summarize these data by finding sample statistics of interest. In this​ case, it would be asking the households how many hours they spend streaming internet video and turning this data into an average. 4. Use the sample statistics to infer the population parameters. In this​ case, based on the data​ gathered, the group estimates the average time per day that a household spends streaming internet video. 5. Draw conclusions to determine what you learned and whether you achieved your goal. In this​ case, we discovered the average time per day that a household spends streaming internet video.

Lesson 11- What is a​ placebo? Describe the placebo effect and how it can make experiments difficult to interpret. How can making an experiment​ single-blind or​ double-blind help?

1. What is a​ placebo? -A placebo lacks the active ingredients of a treatment being tested in a​ study but is identical in appearance to the treatment. 2. Describe the placebo effect and how it can make experiments difficult to interpret. -A situation in which a patient improves simply because they believe they are receiving a useful treatment. It can sometimes be difficult or impossible to distinguish between effects that arise from the actual treatment and those that arise from psychological factors. 3. How can making an experiment​ single-blind or​ double-blind help? -If experiment is​ blinded, then any effect arising from psychological factors should affect all groups equally.

Lesson 11- What is​ bias? How can it affect a statistical​ study? Give examples of bias.

1. What is​ bias? How can it affect a statistical​ study? -Bias refers to any problem in the design or conduct of a statistical study that tends to favor certain results. 2. Give examples of bias. -Non-representative sample -Researcher with a personal stake in the outcome distorts the true meaning of data. -Experiment that is not blinded.

Lesson 11- Why is it so important that a statistical study use a representative​ sample? Briefly describe four common sampling methods.

1. Why is it so important that a statistical study use a representative​ sample? -If the sample fairly represents the population as a​ whole, then it is reasonable to make inferences from the sample to the population. 2. Four (4) common sampling methods. -Simple random​ sampling; Systematic​ sampling; Convenience​ sampling; Stratified sampling

Lesson 12- Consider statistical study where researchers are looking to discover what breed of dog sleeps most. Briefly describe each of the eight guidelines for evaluating statistical studies. Describe how each would apply to a statistical study in which researchers are looking to discover what breed of dog sleeps the most.

1.) First guideline for evaluating statistical study. - Get a big picture view of study. In example​ study, goal is to discover sleeping habits in a population of dogs with an observational study. 2.) Second guideline. - Consider the source. In example​ study, veterinarians have no preference on which breed gets most sleep. 3.) Third guideline. - Look for bias in sample. In example​ study, all breeds were given appropriate sleeping quarters. 4.) Fourth guideline. - Look for problems in defining/measuring variables of interest. In example​ study, sleep is strictly measured according to set guidelines. 5.) Fifth guideline. - Beware of confounding variables. In example​ study, researchers gave dogs the same amount of activity before letting them sleep. 6.) Sixth guideline. - Consider setting & wording in surveys. In example​ study, researchers phrased sleep data in clear wording. 7.) Seventh guideline. - Check results are presented fairly. In example​ study, data supports breed that the researchers claim sleeps the most. 8.) Eighth guideline. - Stand back & consider conclusions. In example​ study, researchers achieved goal of finding which breed of dog sleeps most.

Lesson 12- What are confounding​ variables, & what problems can they​ cause?

1.) What are confounding​ variables? - Items/quantities not intended to be part of study. 2.) What problems can confounding variables​ cause? - Can cause incorrect conclusions to be drawn from the study. - Can cause study to favor certain results unexpectedly.

Lesson 13- Use 4​-point bins ​(96 to 99​, 92 to 95​, etc.) to make frequency table for set of exam scores shown. Include columns for relative frequency & cumulative frequency. 86 90 81 86 77 83 82 87 84 84 89 93 93 84 85 98 81 79 92 95

Complete frequency table below. Scores: Frequency: Relative Frequency: Cumulative Frequency: 96-99 1 5% 1 92-95 4 20% 5 88-91 2 10% 7 84-87 7 35% 14 80-83 4 20% 18 76-79 20 100% 20 Total: 20 100% 20

Lesson 13- A professor records the following final grades in one course. Construct a frequency table for the grades. A A A A A B B B B B B C C C C C C C D D D D F

Complete the table. Grade Frequency: Relative Frequency: Cumulative Frequency: A: 5 20.8% 5 B: 6 25% 11 C: 7 29.2% 18 D: 4 16.7% 22 F: 2 8.3% 24 Total: 24 1=100% 24

Lesson 12- T/F: TV survey got more than 1 million​ phone-in responses, it is clearly more valid than survey by professional​ pollsters, based on interview w/only a few hundred people.

F. Statement does not make sense. Eight guidelines for evaluating statistical study need to be reviewed before one study can be called more valid than another.

Lesson 12- Headline​ "Drugs shown in 98% of​ movies" accompanied news story that described "government study" claiming drug​ use, drinking, or smoking was depicted in​ 98% of top movie rentals. Discuss whether headline accurately represents story.

Headline refers to drugs whereas story refers to​ "drug use,​ drinking, or​ smoking." Headline very misleading bc term​ "drugs" is generally considered to consist of drugs other than cigarettes/alcohol.​ Also, all movies consist of more than just the top movie rentals.

Lesson 12- Y/N: A TV talk show host asks the TV​ audience, "Do you support new national mileage standards for​ automobiles?" & asks people to vote by telephone at a​ toll-free number.

Is there reason to question the​ results? - Yes, there is reason.​ Call-in polls tend to be biased. - ​Yes, there is reason. The TV audience might not be representative of the population. - Yes, there is reason. The wording of the question might produce inaccurate/dishonest responses.

Lesson 11- Y/N In my statistical​ study, I used a sample that was larger than the population.

No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population.

Lesson 11- Determine whether study is observational study or experiment. If study is experiment, identify control & treatment​ groups, & discuss whether​ single- or​ double-blinding is necessary. If study is​ observational, state whether​ case-control study, & if​ so, identify cases & controls. Study at university separated 118 volunteers into​ groups, based on psychological tests designed to determine how often they lied & cheated. Those w/ tendency to lie had different brain structures than those who did not lie.

Observational​ study; case​ control; cases are the volunteers that had a tendency to lie, & the controls are the volunteers that did not lie.

Make a bar graph of populations of 5 most populous states​ (from census​ data) in certain​ country, w/bars in descending order.

State: Population: A 39.8 million B 25.3 million C 21.8 million D 19.8 million E 12.7 million **bar graph is going highest to lowest**

Lesson 11- Determine whether study is observational or experiment. If study is experiment, identify control & treatment​ groups, & discuss whether​ single- or​ double-blinding is necessary. If study is​ observational, state whether a retrospective​ study, & if​ so, identify cases and controls. Using survey of 1533 ppl in country, researchers determined that 83​% of ppl in country believe country is more politically divided than in past & those divisions will persist.

Study is observational. 1. If study is experiment, identify control & treatment groups. - Study not an experiment. 2. If study is experiment, discuss whether​ single- or​ double-blinding necessary. - Study not experiment. 3. If study is​ observational, state whether it's retrospective study. - Study is​ observational, but not retrospective study. 4. If study is retrospective​ study, identify cases & controls. - Study not retrospective.

Lesson 11- Following statistical study gives sample statistic & margin of error. Find confidence interval & answer additional ?'s. Poll conducted day before state election for senator. There are two candidates running for office. Poll results show 55​% of voters favor Republican​ candidate, w/margin of error of 4 percentage points. Should republican expect to​ win? Why/why​ not?

The confidence interval is 51​%-59​%. Republican likely to win bc both endpoints of confidence interval greater than ​50%.

Lesson 11- Following statistical study gives sample statistic & margin of error. Find confidence interval & answer additional ?'s. In survey of 1002 ​ppl, 701 ​(or 70​%) voted particular presidential election. The margin of error for survey was 3 percentage points.​ However, actual voting records show only 59​% of eligible voters actually did vote. Does this imply ppl lied when they responded in survey?

The confidence interval is 67​%-73​%. ​ Does this imply ppl lied when they responded in survey? - Confidence interval doesn't include the 59​% value. If survey conducted​ properly, then unlikely its results would be different from actual​ results, implying either respondents intentionally lied to appear favorable to pollsters or their memories were inaccurate.

Lesson 12- What do we mean by variables of interest in a​ study?

The items or quantities that the study seeks to measure.

Lesson 12- An article noted that chocolate is rich in flavonoids. Article reports, "regular consumption of foods rich in flavonoids may reduce risk of coronary heart​ disease." Study received funding from candy company & chocolate manufacturers association. Identify & explain at least one source of bias in the study described. Then suggest how the bias might have been avoided.

The researchers may have been more inclined to provide favorable results bc funding was provided by party w/definite interest. The bias could have been avoided if researchers were not paid by candy company & chocolate manufacturers.

Lesson 11- U want to determine avg (mean) # of robocalls received/day by adults in New Zealand. Sample​ 1: A set of 521 New Zealanders w/ phone numbers randomly selected from a list of all phone numbers in New Zealand Sample​ 2: The first 521 ppl to visit a particular Auckland grocery store one day. Sample​ 3: The 521 adults in New Zealand who respond to a survey published in a newspaper. Sample​ 4: A set of 521 New Zealanders randomly selected from list of all licensed car owners in New Zealand Which sample is most likely to be a representative​ sample? For each other sample explain why that sample is not likely to be a representative sample.

The sample most likely to be a representative sample is sample 1. 1. Why is sample 1 most likely to be representative​ sample? - List is a random sample not likely biased. 2. Why is sample 2 not likely to be representative​ sample? - Likely biased bc it's limited to geographic region of Auckland. 3. Why is sample 3 not likely to be representative​ sample? - Is convenience sample limited to readers of the newspaper & therefore, likely to be biased. 4. Why is sample 4 not likely to be representative​ sample? - Biased bc it includes only car owners & doesn't include those who cannot afford a car.

Lesson 12- Identify potential sources of bias in following study. An exit poll designed to predict the winner of a local election uses interviews with every Republican who votes between 7:00 and 7:30 a.m.

What sources of​ bias, if​ any, might this study​ have? - Selection bias only.

Lesson 11- To determine mood​, Carolyn divides her day into three​ parts: morning,​ afternoon, & evening. Then measures mood at 2 random times during the day.

What type of sampling used? -Stratified sampling.

Lesson 12- According to newspaper, 26% of Americans rate potatoes their favorite​ vegetable, making it the most popular vegetable.

Which is crucial info that u would want to know before acting on the​ study? - Were respondents given choice of​ potatoes, or did they suggest it without a prompt. - How ? was asked. - How respondents were chosen.

Lesson 12- Much like sound-bytes of news​ stories, statistical studies are often reduced to​ one- or​ two- sentence​ stat-bytes. For following​ stat-byte, discuss what crucial info missing & what more u would want to know before acting on the study. Newspaper reports that over​ 60% of adults avoid dentist because of fear.

Which of the following is crucial info that u would want to know before acting on study? - How respondents were chosen. - The size of the sample. - The ?'s respondents were asked.