1. Intro to Stats and Collecting Data

True or False: If the linear correlation coefficient is close to 0, then the two variables have no relation.

[NW] Television in the Bedroom Is a television (TV) in the bedroom associated with obesity? Researchers questioned 379 twelve-year old adolescents and concluded that the body mass index (BMI) of the adolescents who had a TV in their bedroom was significantly higher than the BMI of those who did not have a TV in their bedroom. Source: Christelle Delmas, Carine Platat, Brigitte Schweitzer, Aline Wagner, Mohamed Oujaa, and Chantal Simon. “Association Between Television in Bedroom and Adiposity Throughout Adolescence,” Obesity, 15:2495–2503, 2007.

What is the response variable in the study? What is the explanatory variable?

In Exercises 4 and 5, determine whether the number is a parameter or a statistic. Explain your reasoning.

In 2021, the median annual salary of a first-year chemist was \$58,700.

Retain Your Knowledge: Decision Making and Hunger Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 normal weight individuals into two groups. All subjects were asked to refrain from eating or drinking (except water) from 11 P.M. on the day prior to their 9 A.M. meeting. At 9 A.M., the subjects were randomly assigned to one of two groups. The subjects in Group 1 were fed breakfast while the subjects in Group 2 were not fed. All subjects were administered a computerized version of an exam that assesses complex decision making under uncertain conditions. The assessment consisted of subjects choosing cards from four decks marked A, B, C, and D. Cards in decks A and B had a point value of 100 while cards in decks C and D had point values of 50. However, deck A had penalty cards that deducted points between 150 and 300; deck B had one penalty card of 1250; deck C had penalty cards between 25 and 75 points; deck D had a single penalty card of 250 points. So, decks A and B had stiffer penalties over the long haul than decks C and D and in the long haul, decks C and D resolted in more points than decks A and B. In total, the subjects would select 100 cards. However, the response variable was the number of cards selected from decks C and D out of the last 60 cards selected. The thinking here is that after 40 card selections, the subjects would be aware of the advantage of decks C and D. The researchers administered a Barret Impulsivity Scale to be sure the two groups did not differ in terms of impolsivity (e.g., “I do things without thinking”). There was no difference in impulsivity, age, or body mass index between the two groups. Before the exam, subjects were asked to report their level of hunger and it was found that Group 2 was significantly more hungry than Group 1. After analysis of the data, it was determined that the mean number of advantageous cards (decks C and D) selected by the subjects in Group 2 was 33.36 cards while the mean was 25.86 for the subjects in Group 1. The researchers concluded that hunger improves advantageous decision making.

e. What role does randomization play in the study? How do the researchers verify that randomization resulted in similar groups prior to the treatment?

Sampling Method The patients were recruited among those at a Veterans Affairs hospital. What type of sampling best describes the way in which the subjects were chosen: simple random sample, systematic sample, convenience sample, stratified sample, cluster sample? Does the method of sampling appear to adversely affect the quality of the results?

Extending Concepts

Golf The distances (in yards) for nine holes of a golf course are listed.

336 393 408 522 147 504 177 375 360

c. Compare the measures you found in part (b) with those found in part (a). What do you notice?

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

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Data Type

c. Identify the level of measurement of the listed earthquake depths: nominal, ordinal, interval, or ratio.

Extending Concepts

Golf The distances (in yards) for nine holes of a golf course are listed.

336 393 408 522 147 504 177 375 360

b. Convert the distances to feet. Then rework part (a).

Reaction Time Researchers wanted to assess the effect of low alcohol consumption on reaction time in seniors, believing that even low levels of alcohol consumption can impair the ability to walk, thereby increasing the likelihood of falling. They identified 13 healthy seniors who were not heavy consumers of alcohol. The experiment took place in late afternoon. Each subject was instructed to have a light lunch and not to drink any caffeinated drinks in the 4 hours prior to arriving at the lab. The seniors were asked to walk on a treadmill on which an obstacle would appear randomly. The reaction time was measured by determining the time it took the senior to lift his or her foot upon the appearance of the obstacle. First, each senior walked the treadmill after consuming a drink consisting of water mixed with orange juice with the scent and taste of vodka. The senior was then asked to drink two additional drinks (40% vodka mixed with orange juice). The senior then walked on the treadmill again. The average response time increased by 19 milliseconds after the alcohol treatment. The researchers concluded that response times are significantly delayed even for low levels of alcohol consumption.

Can you think of any factors that may affect reaction to alcohol that were not controlled?

Pepsi Cans. In Exercises 5–8, refer to the axial loads (pounds) of aluminum Pepsi cans that are 0.0109 in. thick, as listed in Data Set 41 “Aluminum Cans” in Appendix B. An axial load of a can is the maximum weight supported by the side, and it is important to have an axial load high enough so that the can isn’t crushed when the top lid is pressed onto the top. There are seven measurements from each of 25 days of production. If the 175 axial loads are in one column, the first 7 are from the first day, the next 7 are from the second day, and so on, so that the “subgroup size” is 7.

Pepsi Cans: Run Chart Treat the 175 axial loads as a string of consecutive measurements and construct a run chart. What does the result suggest?

Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning.

A survey of 919 college board members found that 89% think that their institution is a good place for members of racial and ethnic minorities. (Source: Association of Governing Boards of Universities and Colleges)

Define the following: Confounding

Determine whether the data are qualitative or quantitative. Explain your reasoning.

Nationalities of passengers on a plane

Green Tea You wonder whether green tea lowers cholesterol.

To research the claim that green tea lowers LDL (so-called bad) cholesterol, you ask a random sample of individuals to divulge whether they are regular green tea users or not. You also obtain their LDL cholesterol levels. Finally, you compare the LDL cholesterol levels of the green tea drinkers to those of the non–green tea drinkers. Explain why this is an observational study.

In Exercises 1–5, use the data listed in the margin, which are magnitudes (Richter scale) and depths (km) of earthquakes from Data Set 24 “Earthquakes” in Appendix B

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Data Type

d. Given that the listed earthquake depths are part of a larger collection of depths, do the data constitute a sample or a population?