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Chapter 14: Problem 15

Name the sampling method that best describes each situation. Choose your answer from the following (A) simple random sampling, (B) convenience sampling, (C) quota sampling, (D) stratified sampling, (E) census. (a) George wants to know how the rest of the class did on the last quiz. He peeks at the scores of a few students sitting right next to him. Based on what he sees, he concludes that nobody did very well. (b) Eureka High School has 400 freshmen, 300 sophomores, 300 juniors, and 200 seniors. The student newspaper conducts a poll asking students if the football coach should be fired. The student newspaper selects 20 freshmen, 15 sophomores, 15 juniors, and 10 seniors for the poll. (c) For the last football game of the season, the coach chooses the three captains by putting the names of all the players in a hat and drawing three names. (Maybe that's why they are trying to fire him!) (d) For the last football game of the season, the coach chooses the three captains by putting the names of all the seniors in a hat and drawing three names.

Short Answer

Expert verified
(a) George used convenience sampling. (b) The student newspaper used stratified sampling. (c) The coach employed simple random sampling. (d) The coach applied quota sampling.

Step by step solution

01

Identify Sampling Method for Scenario (a)

In this scenario, George is choosing the students sitting next to him which is an easy or convenient method for him. So, this is an example of (B) convenience sampling.
02

Identify Sampling Method for Scenario (b)

In this scenario, the student newspaper selects a certain number of students from each grade (freshmen, sophomores, juniors, and seniors). This is a process of classifying the population into strata (or 'groups') and then sampling within these groups. So, this is an example of (D) stratified sampling.
03

Identify Sampling Method for Scenario (c)

In this scenario, the coach takes the names of all the players without any classification or convenience, puts them in a hat and chooses randomly. This is an example of (A) simple random sampling.
04

Identify Sampling Method for Scenario (d)

In this scenario again, the coach picks the names, but this time only from the seniors which shows that a specific group is being targeted. Therefore, this is an example of (C) quota sampling since a specific quota (seniors) is filled by the random drawing.

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Key Concepts

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

Convenience Sampling
When it comes to selecting a sample without much effort or time, convenience sampling is often the go-to method. This technique involves choosing individuals who are easy to reach or contact. It's like going to the nearest table in a restaurant and asking for feedback about the food. This method is quick and inexpensive.

However, convenience sampling has limitations. It might not represent the entire population accurately because it often leaves out many diverse elements. This can lead to biased results, as the sample doesn't reflect all possible perspectives. For instance, if George only checks the scores of the students next to him to guess how the whole class performed, his conclusion might not be correct since he's only looking at a small, easy-to-reach part of the class.
Stratified Sampling
Stratified sampling provides a structured way to ensure that different groups within a population are adequately represented. It involves dividing the population into distinct 'strata' such as age, gender, or in the case of Eureka High School, grade level.

After dividing the population, a sample is taken from each group proportionally. This helps in obtaining a more complete picture of the larger group by including all important subgroups. For example, the high school newspaper wants to represent opinions across all grade levels about the football coach. By using stratified sampling, they can ensure each grade's opinion is considered, making their poll results more reflective of the whole student body.
Simple Random Sampling
Simple random sampling is all about equal opportunity. Every individual from the population has an equal chance of being selected. It's like picking winners from a hat where everyone has tossed in their name. This method is fair and straightforward, as each selection is entirely by chance.

This method's strength lies in its ability to produce a sample that is typically free from bias, representing the population as a whole. In the case of selecting captains for the football team by drawing names from a hat, the coach provides every player with an equal shot, ensuring fairness and randomness in the choice.
Quota Sampling
Quota sampling focuses on filling specific categories or 'quotas' within the sample. It's similar to stratified sampling but with a key difference. Instead of ensuring a random selection within each stratum, quota sampling involves filling a predetermined number of spots.

Consider the scenario of choosing football captains only from senior players. Here, the coach limits the selection pool to seniors and then randomly selects from this group, meeting the 'quota' of seniors to be sampled. This method might not give everyone in the population an equal chance but ensures the sample matches certain characteristics, like age or gender, required for the study.
Educational Statistics
Educational statistics play a vital role in understanding and improving educational systems. These statistics provide insights into various aspects such as performance, demographics, and resources in educational settings.

Using different sampling methods ensures that the data gathered from educational institutions accurately reflects diverse student populations and educational outcomes. For example, stratified sampling might be used to compare test scores across grade levels fairly. Meanwhile, simple random sampling could provide insights into general student satisfaction without bias. By applying statistical methods carefully, educators and policymakers can make informed decisions that lead to improved educational practices and outcomes.

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Most popular questions from this chapter

A big concert was held at the Bowl. Men and women had to go through separate lines to get into the concert (the women had to have their purses checked). Once everyone was inside, total attendance at the concert had to be recorded. The turnstile counters on the female entrance showed a total count of 1542 females, but the turnstile counters on the male entrance were broken and there was no exact record of how many males attended. A sample taken from the 200 seats in Section A showed 121 females and 79 males in that section. Using the numbers from Section A, estimate the total attendance at the concert. (Hint: The proportion of females at the concert should be roughly the same as the proportion of females in Section A.)

Refer to the following story: \(A n\) orange grower wishes to compute the average yield from his orchard. The orchard contains three varieties of trees: \(50 \%\) of his trees are of variety \(A, 25 \%\) of variety \(B,\) and \(25 \%\) of variety \(C .\) (a) Suppose that in his survey, the grower found that each tree of variety A averages 100 oranges, each tree of variety \(\mathrm{B}\) averages 50 oranges, and each tree of variety C averages 70 oranges. Estimate the average yield per tree of his orchard. (b) Is the yield you found in (a) a parameter or a statistic? Explain.

Refer to a study conducted between 2008 and 2010 on the effectiveness of saw palmetto fruit extracts at treating lower urinary tract symptoms in men with prostate enlargement. (Saw palmetto is a widely used over-the-counter supplement for treating urinary tract symptoms.) In the study, 369 men aged 45 years or older were randomly divided into a group taking a daily placebo and a group taking saw palmetto. Participants were nonpaid volunteers recruited at 11 North American sites. All had moderately impaired urinary flow. Because the saw palmetto extract has a mild odor, the doses were administered using gelcaps to eliminate the odor. In an analysis of the 306 men who completed the 72 -week trial, both groups had similar small improvements in mean symptom scores, but saw palmetto conferred no benefit over placebo on symptom scores or on any secondary outcomes. If you were a 55 -year-old male with an enlarged prostate taking saw palmetto daily, how might you react to this study?

Refer to the following story (see also Exercise 32): The Dean of Students at Tasmania State University wants to determine how many undergraduates at TSU are familiar with a new financial aid program offered by the university. There are 15,000 undergraduates at \(T S U,\) so it is too expensive to conduct a census. The following sampling method, known as systematic sampling, is used to choose a representative sample of undergraduates to poll. Start with the registrar's alphabetical listing containing the names of all undergraduates. Randomly pick a number between 1 and \(100,\) and count that far down the list. Take that name and every 100 th name after it. For example, if the random number chosen is \(73,\) then pick the \(73 \mathrm{rd}, 173 \mathrm{rd}, 273 \mathrm{rd},\) and so forth, names on the list. (a) Find the sampling proportion. (b) Suppose that the survey had a response rate of \(90 \%\). Find the size \(n\) of the sample.

Imagine you have a very large coin jar full of nickels, dimes, and quarters. You would like to know how much money you have in the jar, but you don't want to go through the trouble of counting all the coins. You decide to estimate how many nickels, dimes, and quarters are in the jar using the capture- recapture method. After shaking the jar well, you draw a first sample of 150 coins and get 36 quarters, 45 nickels, and 69 dimes. Using a permanent ink marker you tag each of the 150 coins with a black dot and put the coins back in the jar, shake the jar really well to let the tagged coins mix well with the rest, and draw a second sample of 100 coins. The second sample has 28 quarters, 29 nickels, and 43 dimes. Of these, 4 quarters, 5 nickels, and 8 dimes have black dots. Estimate how much money is in the jar. (Hint: You will need a separate calculation for estimating the quarters, nickels, and dimes in the jar.)
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