Solved: Retirement Planning The Principal Financial Group

Problem 1AYU Define statistics.

Explain the difference between a population and a sample.

Problem 3AYU A(n) ________ is a person or object that is a member of the population being studied.

___________ statistics consists of organizing and summarizing information collected, while ________ statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

A(n) ________ is a numerical summary of a sample. A(n) ________ is a numerical summary of a population.

Problem 6AYU ___________ are the characteristics of the individuals of the population being studied.

In Problems 7-14, Determine whether the underlined value is a parameter or a statistic. State Government Following the 2010 national midterm election, 18% of the governors of the 50 United States were female. Source: National Governors Association

In Problems 7-14, Determine whether the underlined value is a parameter or a statistic. Calculus Exam The average score for a class of 28 students taking a calculus midterm exam was 72%.

Determine whether the underlined value is a parameter or a statistic. School Bullies In a national survey of 1300 high school students (grades 9 to 12), 32% of respondents reported that someone had bullied them at school. Source: Bureau of Justice Statistics

In Problems 7-14, Determine whether the underlined value is a parameter or a statistic. Drug Use In a national survey on substance abuse, 10.0% of respondents aged 12 to 17 reported using illicit drugs within the past month.

Determine whether the underlined value is a parameter or a statistic. Moonwalkers Only 12 men have walked on the moon. The average age of these men at the time of their moonwalks was 39 years, 11 months, 15 days.

Problem 13AYU In Problems Determine whether the underlined value is a parameter or a statistic. Hygiene Habits A study of 6076 adults in public rest rooms (in Atlanta, Chicago, New York City, and San Francisco) found that 23% did not wash their hands before exiting.

Determine whether the underlined value is a parameter or a statistic. Public Knowledge Interviews of 100 adults 18 years of age or older, conducted nationwide, found that 44% could state the minimum age required for the office of U.S. president.

Classify the variable as qualitative or quantitative. Nation of origin

In Problems 15-22, classify the variable as qualitative or quantitative. Number of siblings

Classify the variable as qualitative or quantitative. Grams of carbohydrates in a doughnut

Classify the variable as qualitative or quantitative. Number on a football player’s jersey

In Problems 15-22, classify the variable as qualitative or quantitative. Number of unpopped kernels in a bag of ACT microwave popcorn

In Problems 15-22, classify the variable as qualitative or quantitative. Assessed value of a house

Problem 21AYU In Problems classify the variable as qualitative or quantitative. Phone number

Classify the variable as qualitative or quantitative. Student ID number

Problem 23AYU In Problems determine whether the quantitative variable is discrete or continuous. Goals scored in a season by a soccer player

In Problems 23-30, determine whether the quantitative variable is discrete or continuous. Volume of water lost each day through a leaky faucet

In Problems 23-30, determine whether the quantitative variable is discrete or continuous. Length (in minutes) of a country song

Problem 26AYU In Problems determine whether the quantitative variable is discrete or continuous. Number of Sequoia trees in a randomly selected acre of Yosemite National Park

Determine whether the quantitative variable is discrete or continuous. Temperature on a randomly selected day in Memphis, Tennessee

Problem 28AYU In Problems determine whether the quantitative variable is discrete or continuous. Internet connection speed in kilobytes per second

Determine whether the quantitative variable is discrete or continuous Points scored in an NCAA basketball game

Determine whether the quantitative variable is discrete or continuous. Air pressure in pounds per square inch in an automobile tire

Problem 31AYU In Problems, In Problems Determine the level of measurement of each variable. Nation of origin

Problem 32AYU In Problems, In Problems Determine the level of measurement of each variable. Movie ratings of one star through five stars

Problem 33AYU In Problems, In Problems Determine the level of measurement of each variable. Volume of water used by a household in a day

Problem 34AYU In Problems, In Problems Determine the level of measurement of each variable. Year of birth of college students

Problem 35AYU In Problems, In Problems Determine the level of measurement of each variable. Highest degree conferred (high school, bachelor’s, and so on)

In Problems, In Problems Determine the level of measurement of each variable. Eye color

In Problems 31-38, determine the level of measurement of each variable. Assessed value of a house

In Problems 31-38, Determine the level of measurement of each variable. Time of day measured in military time

In Problems 39-44, a research objective is presented. For each, identify the population and sample in the study. The Gallup Organization contacts 1028 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had been prescribed medications for any mental disorders, such as depression or anxiety.

Problem 40AYU In Problem, a research objective is presented. For each, identify the population and sample in the study. A quality-control manager randomly selects 50 bottles of Coca-Cola that were filled on October 15 to assess the calibration of the filling machine.

In Problem, a research objective is presented. For each, identify the population and sample in the study. A farmer wants to learn about the weight of his soybean crop. He randomly samples 100 plants and weighs the soybeans on each plant.

In this problem, a research objective is presented. For each, identify the population and sample in the study. Every year the U.S. Census Bureau releases the Current Population Report based on a survey of 50,000 households. The goal of this report is to learn the demographic characteristics of all households within the United States, such as income.

Problem 43AYU In Problem, a research objective is presented. For each, identify the population and sample in the study. Folate and Hypertension Researcher John P. Forman and co-workers want to determine whether or not higher folate intake is associated with a lower risk of hypertension (high blood pressure) in younger women (27 to 44 years of age). To make this determination, they look at 7373 cases of hypertension in younger women and find that younger women who consume at least 1000 micrograms per day (?g/d) of total folate (dietary plus supplemental) had a decreased risk of hypertension compared with those who consume less than 200 mg/d. Source: John P. Forman, MD; Eric B. Rimm, ScD; Meir J. Stampfer, MD; Gary C. Curhan, MD, ScD, “Folate Intake and the Risk of Incident Hypertension among US Women,” Journal of the American Medical Association 293:320–329, 2005

In Problems 39-44, a research objective is presented. For each, identify the population and sample in the study. A large community college notices that an increasing number of full-time students are working while attending the school. The administration randomly selects 128 students and asks this question: How many hours per week do you work?

In Problems 45-48, Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. Smart Phones. The following represent information on smart phones recommended by CNET.

In Problems 45-48, identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. BMW Cars The following information relates to the 2011 model year product line of BMW automobiles.

In Problems 45-48, identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. Driver’s License Laws The following data represent driver’s license laws for various states.

Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete. MP3 Players The following represent information on MP3 players recommended by CNET.

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 non-smokers. 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. Source: Weiser, M., Zarka, S. Werbeloff, N., Kravitz, E. and Lubin, G. (2010). "Cognitive Test Scores in Male Adolescent Cigarette Smokers Compared to Non-smokers: A Population-Based Study." Addiction. 105:358–363. doi: 10.1111/j.1360-0443.2009.02740.x) (a) What is the research objective? (b) What is the population being studied? What is the sample? (c) What are the descriptive statistics? (d) What are the conclusions of the study?

Problem 50AYU A Cure for the Common Wart A study conducted by researchers was designed “to determine if application of duct tape is as effective as cryotherapy (liquid nitrogen applied to the wart for 10 seconds every 2 to 3 weeks) in the treatment of common warts.” The researchers randomly divided 51 patients into two groups. The 26 patients in group 1 had their warts treated by applying duct tape to the wart for 6.5 days and then removing the tape for 12 hours, at which point the cycle was repeated for a maximum of 2 months. The 25 patients in group 2 had their warts treated by cryotherapy for a maximum of six treatments. Once the treatments were complete, it was determined that 85% of the patients in group 1 and 60% of the patients in group 2 had complete resolution of their warts. The researchers concluded that duct tape is significantly more effective in treating warts than cryotherapy. Source: Dean R. Focht III, Carole Spicer, Mary P. Fairchok. “The Efficacy of Duct Tape vs. Cryotherapy in the Treatment of Verruca Vulgaris (The Common Wart),” Archives of Pediatrics and Adolescent Medicine, 156(10), 2002 (a) What is the research objective? ________________ (b) What is the population being studied? What is the sample? ________________ (c) What are the descriptive statistics? ________________ (d) What are the conclusions of the study?

Problem 51AYU Government Waste Gallup News Service conducted a survey of 1026 American adults aged 18 years or older, August 31–September, 2, 2009. The respondents were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., how many cents of each dollar would you say are wasted?” Of the 1026 individuals surveyed, 35% indicated that 51 cents or more is wasted. Gallup reported that 35% of all adult 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. (a) What is the research objective? ________________ (b) What is the population? ________________ (c) What is the sample? ________________ (d) List the descriptive statistics. ________________ (e) What can be inferred from this survey?

Retirement Planning The Principal Financial Group conducted a survey of 1172 employees in the United States between July 28, 2010, and August 8, 2010, and asked if they were currently participating in the employer-sponsored automatic payroll deduction for a 401(k) plan to save for retirement. Of the 1172 employees surveyed, 27% indicated they were participating. The Principal Group reported that 27% of all employees in the United States participate in automatic payroll deduction for 401(k) plan to save for retirement with a 4% margin of error and 95% confidence. (a) What is the research objective? (b) What is the population? (c) What is the sample? (d) List the descriptive statistics. (e) What can be inferred from this survey?

Interpreting the Variable Suppose a fundraiser holds a raffle for which each person who enters the room receives a ticket. The tickets are numbered 1 to N, where N is the number of people at the fundraiser. The first person to arrive receives ticket number 1, the second person receives ticket number 2, and so on. Determine the level of measurement for each of the following interpretations of the variable ticket number. (a) The winning ticket number. (b) The winning ticket number was announced as 329. An attendee noted his ticket number was 294 and stated, “I guess I arrived too early.” (c) The winning ticket number was announced as 329. An attendee looked around the room and commented, “It doesn’t look like there are 329 people in attendance.”

Analyze the Article Read the newspaper article and identify (a) the research question the study addresses, (b) the population, (c) the sample, (d) the descriptive statistics, and (e) the inferences of the study.

Contrast the differences between qualitative and quantitative variables.

Discuss the differences between discrete and continuous variables.

Problem 58AYU In your own words, define the four levels of measurement of a variable. Give an example of each.

Problem 59AYU Explain what is meant when we say “data vary.” How does this variability affect the results of statistical analysis?

Explain the process of statistics.

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