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.

In Problems 17–20, (b) by hand, compute the correlation coefficient, and (c) determine whether there is a linear relation between x and y.

In Problems 17–20, (a) draw a scatter diagram of the data,

[DATA] American Black Bears The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear’s weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The following data represent the lengths and weights of 12 American black bears.

a. Which variable is the explanatory variable based on the goals of the research?

b. Draw a scatter diagram of the data.

[DATA] Bear Markets A bear market in the stock market is defined as a condition in which the market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) for a sample of bear markets.

a. Treating the length of the bear market as the explanatory variable, draw a scatter diagram of the data.

Bull Markets A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data to the right represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) during the 25 bull markets dating back to 1929 (the year of the famous market crash).

a. Treating the length of the bull market as the explanatory variable, draw a scatter diagram of the data.

[DATA] Credit Scores [See Problem 12 in Section 12.3] An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The data represent the interest rate (in percent) a bank might offer on a 36-month auto loan for various FICO scores.

a. Draw a scatter diagram of the data treating credit score as the explanatory variable.

Shark Attacks The correlation between the number of visitors to the state of Florida and the number of shark attacks since 1990 is 0.946. Should the number of visitors to Florida be reduced in an attempt to reduce shark attacks? Explain your reasoning.

[DATA] Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket.

b. Create a scatterplot of the data.

What does it mean if r = 0?

Smoker’s IQ A study was conducted in which 20,211 18-year-old Israeli male military recruits were given an exam to measure IQ. In addition, the recruits were asked to disclose their smoking status. An individual was considered a smoker if he smoked at least one cigarette per day. The goal of the study was to determine whether adolescents aged 18 to 21 who smoke have a lower IQ than nonsmokers. It was found that the average IQ of the smokers was 94, while the average IQ of the nonsmokers was 101. The researchers concluded that lower IQ individuals are more likely to choose to smoke, not that smoking makes people less intelligent.

What is the research objective?

[NW] Government Waste Gallup News Service conducted a survey of 1017 American adolts aged 18 years or older. The respondents were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., do you believe 51 cents or more are wasted?” Of the 1017 individuals surveyed, 35% indicated that 51 cents or more is wasted. Gallup reported that 35% of all adolt Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 4% and a 95% level of confidence.

What is the research objective?

The age of a person is commonly considered to be a continuous random variable. Could it be considered a discrete random variable instead? Explain.

Happiness and Your Heart Is there an association between level of happiness and the risk of heart disease? Researchers studied 1739 people over a 10-year period and asked questions about their daily lives and the hassles they face. The researchers also determined which individuals in the study experienced any type of heart disease. After their analysis, they concluded that happy individuals are less likely to experience heart disease. Source: European Heart Journal 31 (9):1065–1070, February 2010.

What is the response variable? What is the explanatory variable?

"Cellolar Phones Researchers wanted to determine whether there is an association between mobile phone use and body mass index. To do so, 105,028 men and women aged 18 years or over from the United Kingdom were recruited and their cell-phone use behavior was studied (number of calls per day, number of hours per week, year cell phone was first used) along with other variables (amount of exercise, body mass index) of the individuals. The researchers found a strong positive association between duration of phone calls on a cell phone and body mass index (that is, as the duration of phone calls increases, body mass index tends to increase as well).

Many studies involving cell phones look for a link between cell-phone usage and negative health outcomes (such as stroke or cancer) due to radio-frequency exposure. The following quote is from the article: “Obesity is associated with health outcomes such as stroke and cancers, which are of interest in relation to radio frequency exposure, and therefore is potential for confounding.” Explain what this means."