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Chapter 1: Problem 20

Data from a poll conducted by Travelocity led to the following estimates: Approximately \(40 \%\) of travelers check their work e-mail while on vacation; about \(33 \%\) take their cell phones on vacation to stay connected with work; and about \(25 \%\) bring their laptops on vacation (San Luis Obispo Tribune, December 1,2005 ). Are the given percentages statistics or population characteristics?

Short Answer

Expert verified
The given percentages are statistics, not population characteristics, because they were derived from a sample of travelers, not the entire population of travelers.

Step by step solution

01

Definition of Statistics and Population Characteristics

Let's start by defining the key terms: Statistics and population characteristics. A statistic is a numerical characteristic of a sample, whereas a population characteristic (or a parameter) is a numerical characteristic of a population. This distinction will help to answer the questions.
02

Understand the nature of data

The data provided is based on a poll conducted by Travelocity, and these percentages refer to the surveyed sample, not the whole population of all travelers.
03

Determine whether the data is a statistic or a population characteristic

Since the data are derived from a sample and not the total population, these percentages are examples of statistics, not population characteristics.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population Characteristics
Population characteristics, also known as parameters, describe traits or features that belong to an entire group or population. In statistics, we often deal with a vast group, such as all travelers worldwide. When we refer to a characteristic of the whole population, we're discussing a parameter.

For instance, imagine we're interested in knowing the exact percentage of every single traveler who checks their email during vacations. The true percentage that reflects this behavior across all travelers would be a population characteristic. However, measuring characteristics for entire populations is often impractical, if not impossible, because of their size.

It's essential to note that because population parameters involve data from every member of the population, they provide an exact figure for the characteristic being measured. Unfortunately, reaching the true value of a population parameter is challenging without surveying everyone, which is where sample data comes in handy.
Sample Data
Sample data is collected from a smaller segment of a larger population. Think of it as a mini-version of the population. This data represents a limited group of individuals within the larger population, making it much easier to collect and analyze.

In our example, Travelocity conducted a poll among travelers, representing only a fraction of all travelers. The percentages they provided, such as the 40% who check work emails, are derived from these sample data and not the entire traveler population.

Sample data help us make observations and inferences about the population without having to survey everyone. However, the results can vary based on who is included in the sample, so choosing a representative sample is crucial to accurately reflect the population's characteristics.
Parameters
When we talk about parameters, we're discussing values that precisely describe a population. These parameters are the real figures behind concepts like percentage or mean for the entire group.

For instance, the population parameter of interest might be the true percentage of all travelers checking work emails while on vacation. This true value is often hard to determine directly because it requires polling every single traveler, hence why researchers rely on samples.

The distinction between parameters and statistics is crucial in statistical analysis:
  • Parameters give us the actual measure of our interest within the whole population.
  • Statistics estimate the parameters using sample data.
Although we use sample data to estimate parameters, remember that parameters are ideal values that would appear if a complete census were possible.

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Most popular questions from this chapter

The paper "From Dr. Kildare to Grey's Anatomy" (Annals of Emergency Medicine [2010]: \(21 \mathrm{~A}-23 \mathrm{~A}\) ) describes several studies of how the way in which doctors are portrayed on television might influence public perception of doctors. One study was described as follows: Rebecca Chory, Ph.D., now an associate professor of communication at West Virginia University, began studying the effect of such portrayals on patients' attitudes toward physicians. Using a survey of 300 undergraduate students, she compared perceptions of physicians in 1992 - the end of the era when physicians were shown as all-knowing, wise father figures-with those in \(1999,\) when shows such as \(E R\) and Chicago Hope \((1994-2000)\) were continuing the transformation to showing the private side and lives of physicians, including vivid demonstrations of their weaknesses and insecurities. Dr. Chory found that, regardless of the respondents' personal experience with physicians, those who watched certain kinds of television had declining perceptions of physicians' composure and regard for others. Her results indicated that the more prime time physician shows that people watched in which physicians were the main characters, the more uncaring, cold, and unfriendly the respondents thought physicians were. a. Answer the following four questions for the observational study described in this exercise. (Hint: Reviewing Examples 1.3 and 1.4 might be helpful.) 1\. What is the population of interest? 2\. Was the sample selected in a reasonable way? 3\. Is the sample likely to be representative of the population of interest? 4\. Are there any obvious sources of bias? b. Based on the study design, do you think that the stated conclusions are reasonable?

According to the article "Rubbing Hands Together Under Warm Air Dryers Can Counteract Bacteria Reduction" (Infectious Disease News, September 22,2010 ), washing your hands isn't enough-good "hand hygiene" also includes drying hands thoroughly. The article described an experiment to compare bacteria reduction for three different hand-drying methods. In this experiment, subjects handled uncooked chicken for 45 seconds, then washed their hands with a single squirt of soap for 60 seconds, and then used one of the three hand-drying methods. The bacteria count on their hands was then measured. Suppose you want to carry out a similar experiment with 30 subjects who are willing to participate. Describe a method for randomly assigning each of the 30 subjects to one of the hand-drying methods.

1.32 In an experiment to compare two different surgical procedures for hernia repair ("A Single-Blinded, Randomized Comparison of Laparoscopic Versus Open Hernia Repair in Children," Pediatrics [2009]: 332-336), 89 children were assigned at random to one of the two surgical methods. The methods studied were laparoscopic repair and open repair. In laparoscopic repair, three small incisions are made, and the surgeon works through these incisions with the aid of a small camera that is inserted through one of the incisions. In the open repair, a larger incision is used to open the abdomen. One of the response variables was the amount of medication given after the surgery to control pain and nausea. The paper states, "For postoperative pain, rescue fentanyl \((1 \mathrm{mg} / \mathrm{kg})\) and for nausea, ondansetron \((0.1 \mathrm{mg} / \mathrm{kg})\) were given as judged necessary by the attending nurse blinded to the operative approach." a. Why do you think it was important that the nurse who administered the medications did not know which type of surgery was performed? b. Explain why it was not possible for this experiment to be double-blind.

Use the following information to answer. Many surgeons play music in the operating room. Does the type of music played have an effect on the surgeons' performance? The report "Death Metal in the Operating Room" (NPR, Dec. 24, 2009, www.npr.org) describes an experiment in which surgeons used a simulator to perform a surgery. Some of the surgeons listened to music with vocal elements while performing the surgery, and others listened to music that did not have vocal elements. The researchers concluded that the average time to complete the surgery was greater when music with vocal elements is played than when music without vocal elements is played. 1.43 Could this experiment have been double-blind? Explain why or why not.

Use the following information to answer. The paper "Turning to Learn: Screen Orientation and Reasoning from Small Devices" (Computers in Human Behavior [2011]: \(793-797\) ) describes a study that investigated whether cell phones with small screens are useful for gathering information. The researchers wondered if the ability to reason using information read on a small screen was affected by the screen orientation. The researchers assigned 33 undergraduate students who were enrolled in a psychology course at a large public university to one of two groups at random. One group read material that was displayed on a small screen in portrait orientation, and the other group read material on the same size screen but turned to display the information in landscape orientation (see the following figure). Is the study described an observational study or an experiment?
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