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Chapter 4: Problem 68

What's your favorite poem? In fall \(1995,\) the \(\mathrm{BBC}\) in Britain requested viewers to call the network and indicate their favorite poem. Of 7500 callers, more than twice as many voted for Rudyard Kipling's If than for any other poem. The \(\mathrm{BBC}\) then reported that this was the clear favorite. a. Since any person could call, was this sample a simple random sample? Explain. b. Was this a volunteer sample? Explain. c. If the BBC truly wanted to determine Brits' favorite poem, how could they do so more reliably?

Short Answer

Expert verified
a. No, it's not a simple random sample. b. Yes, it is a volunteer sample. c. Use stratified random sampling for more reliable results.

Step by step solution

01

Evaluate Simple Random Sample Criteria

A simple random sample is one where each individual in the entire population has an equal chance of being selected. In this case, people chose to call the BBC on their own. They were not randomly selected or contacted by the BBC. Therefore, it does not meet the criteria for a simple random sample.
02

Determine If It's a Volunteer Sample

A volunteer sample consists of individuals who choose to participate on their own accord. In this scenario, the callers decided to call the BBC voluntarily to register their favorite poem. This is a clear example of a volunteer sample, as the participants were self-selected.
03

Suggest a More Reliable Sampling Method

To determine the favorite poem more reliably, the BBC could use a stratified random sampling method. This method involves dividing the British population into different subgroups (strata) such as age, sex, or region, and then randomly sampling from each subgroup. This ensures a more representative sample of the entire population.

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Key Concepts

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

Simple Random Sample
A Simple Random Sample (SRS) is a method where every individual in the population has an equal chance of being selected. This technique is akin to drawing names from a hat, where each person has the same likelihood of being chosen. The magic of a simple random sample lies in its ability to produce representative snapshots of the whole population.

Imagine you want to determine the favorite ice cream flavor in a city. With a simple random sample, you鈥檇 ensure each city resident has an equal probability of being selected for your taste test. This way, everyone鈥攆rom young kids to seniors鈥攈as an equal voice. However, in the BBC case, they did not utilize a simple random sample. People called in voluntarily. This means not everyone had an equal chance to present their choice, as it solely depended on who decided to participate.
Volunteer Sample
A Volunteer Sample is when participants opt in to be part of a survey or study on their own accord. Unlike a structured random sample, a volunteer sample can lead to biased results.

The bias occurs because the type of people who voluntarily decide to participate may share specific common characteristics that are not representative of the entire population. Think of a street musician asking for song preferences; fans of the genre played are more likely to stop and comment than those who don't enjoy it.
  • This can skew the data toward certain preferences.
  • It's like using a Facebook poll and assuming everyone on the internet feels the same way as your immediate friends or followers.
In the original exercise concerning the BBC, because callers were self-selected, the responses may reflect the opinions of those particularly enthusiastic about poetry, rather than the general British population鈥檚 favorite poem.
Stratified Random Sampling
Stratified Random Sampling offers a more comprehensive and accurate glimpse at the preferences of an entire population by ensuring representation from all critical segments. This approach divides the target population into distinct subgroups, or strata, such as age groups, geographic locations, or income levels. Once the population is divided, random samples are taken from each subgroup.

Why choose stratified over simple random sampling? It mitigates the risk of getting skewed results due to small, unrepresentative samples. If each group in a population varies significantly in some important respect, stratified sampling ensures that variations get captured in the final analysis.
  • For the BBC's quest to find Britain's favorite poem, they could have divided the population by age, region, or literary preference.
  • From each category, people would be randomly selected, ensuring varied and comprehensive input.
This technique helps in painting a more nuanced and reliable picture of the societal trends or preferences.

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Most popular questions from this chapter

Unethical experimentation Give an example of a scientific question of interest for which it would be unethical to conduct an experiment. Explain how you could instead conduct an observational study.

Chocolate good for you? A few studies published in 2007 claimed health benefits from eating dark chocolate or drinking cocoa. One study found much lower rates of death due to cancer among the Kuna Indians, who live in the San Blas islands of Panama and drink cocoa as their main beverage, compared to residents of mainland Panama (V. Bayard et al., Int. J. Med. Sci., 2007; 4: \(53-58)\) a. Identify the response variable and the explanatory variable. b. Was this study an observational study or an experimental study? Explain.

Colds and vitamin \(\mathbf{C}\) For some time there has been debate about whether regular large doses of vitamin \(\mathrm{C}\) reduce the chance of getting a common cold. a. Explain how you could design an experiment to test this. Describe all parts of the experiment, including (i) what the treatments are, (ii) how you assign subjects to the treatments, and (iii) how you could make the study double-blind. b. An observational study indicates that people who take vitamin \(\mathrm{C}\) regularly get fewer colds, on the average. Explain why these results could be misleading.

Two factors helpful? A two-factor experiment designed to compare two diets and to analyze whether results depend on gender randomly assigns 20 men and 20 women to the two diets, 10 of each to each diet. After three months the sample mean weight losses are as shown in the table. Caffeine jolt A study (Psychosomatic Medicine 2002 ; \(64: 593-603)\) claimed that people who consume caffeine regularly may experience higher stress and higher blood pressure. In the experiment, 47 regular coffee drinkers consumed 500 milligrams of caffeine in a pill form (equivalent to four 8 -oz cups) during one workday, and a placebo pill during another workday. The researchers monitored the subjects' blood pressure and heart rate, and the subjects recorded how stressed they felt. a. Identify the response variable(s), explanatory variable, experimental units, and the treatments. b. Is this an example of a completely randomized design, or a crossover design? Explain.

Capture-recapture Biologists and naturalists often use sampling to estimate sizes of populations, such as deer or fish, for which a census is impossible. Capture-recapture is one method for doing this. A biologist wants to count the deer population in a certain region. She captures 50 deer, tags each, and then releases them. Several weeks later, she captures 125 deer and finds that 12 of them were tagged. Let \(N=\) population size, \(M=\) size of first sample, \(n=\) size of second sample, \(R=\) number tagged in second sample. The table shows how results can be summarized. a. Identify the values of \(M, n,\) and \(R\) for the biologist's experiment. b. One way to estimate \(N\) lets the sample proportion of tagged deer equal the population proportion of tagged deer. Explain why this means that $$ \frac{R}{n}=\frac{M}{N} $$ and hence that the estimated population size is \(N=(M \times n) / R\) c. Estimate the number of deer in the deer population using the numbers given. d. The U.S. Census Bureau uses capture-recapture to make adjustments to the census by estimating the undercount. The capture phase is the census itself (persons are "tagged" by having returned their census form and being recorded as counted) and the recapture phase (the second sample) is the postenumerative survey (PES) conducted after the census. Label the table in terms of the census application.
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