/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 16 An audit is performed on last ye... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 16

An audit is performed on last year's 15,000 student-aid packages given out by the financial aid office at Tasmania State University. Roughly half of the student-aid packages were less than \(\$ 1000\) (Category 1 ), about one-fourth were between \(\$ 1000\) and \(\$ 5000\) (Category 2 ), and another quarter were over \(\$ 5000\) (Category 3 ). For each audit described below, name the sampling method that best describes it. Choose your answer from the following: (A) simple random sampling, (B) convenience sampling, (C) quota sampling, (D) stratified sampling, (E) census. (a) The auditor reviews all 15,000 student-aid packages. (b) The auditor selects 200 student-aid packages in Category 1,100 student-aid packages in Category \(2,\) and 100 student-aid packages in Category \(3 .\) (c) The auditor reviews the first 500 student-aid packages that he comes across. (d) The auditor first separates the student- aid packages by school (Agriculture, Arts and Humanities, Engineering, Nursing, Social Science, Science, and Mathematics). Three of these schools are selected at random and further subdivided by major. Ten majors are randomly selected within each selected school, and then 20 students are randomly selected from each of the selected majors.

Short Answer

Expert verified
(a) Census, (b) Quota sampling, (c) Convenience sampling, (d) Stratified sampling.

Step by step solution

01

Understanding the sampling methods

Simple random sampling is when each item in a population has an equal chance of being selected. Convenience sampling is a non-probabilistic method where samples are selected because of their convenient accessibility and proximity to the researcher. Quota sampling is a method where the population is divided into groups (or 'quotas') and samples are collected from each group to reach a target. Stratified sampling divides the population into distinct groups (or 'strata') and selects samples from these groups independently. A census refers to a complete enumeration of all items in the population which means it includes every member of the population.
02

Identify the sampling method for scenario (a)

Given the scenario - 'The auditor reviews all 15,000 student-aid packages', this can be categorized as a census, because every member of the population is being studied.
03

Identify the sampling method for scenario (b)

Given the scenario - 'The auditor selects 200 student-aid packages in Category 1, 100 student-aid packages in Category 2, and 100 student-aid packages in Category 3', this corresponds to the method of quota sampling. Here the auditor is pre-determining the quantity of student aid packages to sample from each category.
04

Identify the sampling method for scenario (c)

Given the scenario - 'The auditor reviews the first 500 student-aid packages that he comes across', this is an example of a convenience sampling because sampling is done in a way that is convenient to the auditor.
05

Identify the sampling method for scenario (d)

Given the scenario - 'The auditor first separates the student-aid packages by school...and then 20 students are randomly selected from each of the selected majors', this is an example of stratified sampling. The population is divided into different groups (in this case, schools, and then majors within schools) and samples are taken from each of these groups.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Simple Random Sampling
Simple random sampling is akin to each name in a hat having an equal chance of being pulled out. In this method, every member of a population has an equal and random chance of being selected for study. This makes it one of the most straightforward and unbiased sampling techniques. This sampling method is beneficial when a sample needs to be representative of the entire population. However, it can be challenging to implement in large populations. To achieve true randomness, computerized programs are often used because they can efficiently shuffle and select samples without human bias. Using simple random sampling helps in reducing selection bias and ensuring that each subgroup within a population has a fair chance of being represented in the sample.
Convenience Sampling
Convenience sampling is like picking the low-hanging fruit; it's easy and fast, but not necessarily representative. This method selects samples because they are easily accessible to the researcher. For instance, a researcher may choose participants who are nearby or readily available. While it is the simplest and least expensive method of sampling, convenience sampling involves a high degree of bias. This bias stems from the non-random selection process, which might not accurately represent the entire population.
  • Pros: Easy to conduct and cost-effective.
  • Cons: Highly prone to bias and less reliable.
This method is often used in preliminary studies or when other sampling methods are impractical or unnecessary.
Quota Sampling
Quota sampling involves setting quotas or targets for a sample鈥攖he researcher predetermines the specific number of subjects from each group or category. This method ensures representation from various subgroups according to predefined criteria. Unlike stratified sampling, quota sampling does not use random selection. Instead, researchers fill the quota by selecting subjects that fit the criteria until the quota is met.
  • Usable for ensuring coverage across different segments of a population.
  • Helps in collecting data from specific subgroups without needing access to the entire population.
However, this method does not eliminate selection bias since it relies on the researcher鈥檚 discretion to fill the quotas.
Stratified Sampling
Stratified sampling is a more structured approach than simple random sampling. In this method, the population is divided into different subgroups or 'strata', and samples are taken from each stratum independently. The goal of stratified sampling is to ensure that each subgroup is adequately represented. This technique is particularly useful when a population has distinct groups, and you want to ensure representation of all those groups in the sample.
  • Stratified sampling can reduce sampling error by ensuring representation across various segments.
  • Ideal for populations with significant diversity within different subgroups.
Researchers often use this method to get a more accurate reflection of a population's full range.
Census
A census is a comprehensive data collection method that involves gathering information from every member of a population. Unlike sampling methods that analyze a subset, a census considers everyone, leaving no room for sampling error. Conducting a census can be resource-intensive in terms of time and cost; it is often used when the stakes are high and requires complete accuracy, like in national population censuses.
Common contexts for implementing a census include government statistics, public health studies, or any situation where absolute data completeness is critical.
Data Collection in Education
Data collection in education involves gathering relevant and accurate data to understand and improve educational systems. Various methods can be employed, ranging from surveys, standardized tests, to observational studies, each suited to different kinds of information needs. Collecting data effectively can help educators to:
  • Analyze student performance and highlight areas for improvement.
  • Inform policy-making to enhance educational infrastructures.
  • Ensure that resources are appropriately allocated.
Ultimately, robust data collection can lead to better educational outcomes and more informed decision-making.
Educational Statistics
Educational statistics play an essential role in analyzing data collected from educational settings. These statistics provide a quantitative foundation for understanding trends, outcomes, and challenges within education. They are used to:
  • Measure the effectiveness of instructional methods.
  • Evaluate the performance of educational programs.
  • Inform stakeholders such as educators, policymakers, and parents.
By using educational statistics, stakeholders can make data-driven decisions that support better educational environments and outcomes for students.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

To count whale populations, the "capture" is done by means of a photograph, and the "tagging" is done by identifying each captured whale through their unique individual pigmentation and markings. To estimate the population of gray whales in a region of the Pacific between Northern California and Southeast Alaska, 121 gray whales were "captured" and "tagged" in \(2007 .\) In 2008,172 whales were "recaptured." Of these, 76 had been "tagged" in the 2007 survey. Based on these figures, estimate the population of gray whales in the region. [Source: Calambokidis, J., J.L. Laake and A. Klimek, "Abundance and population structure of seasonal gray whales in the Pacific Northwest, 1998 - 2008." Paper IWC/62/BRG32 submitted to the International Whaling Commission Scientific Committee, \(2010 .\)

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) Explain why the method used for choosing the sample is not simple random sampling. (b) If \(100 \%\) of those responding claimed that they were not familiar with the new financial aid program offered by the university, is this result more likely due to sampling variability or to sample bias? Explain.

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.)

Refer to the following story: The city of Cleansburg has 8325 registered voters. There is an election for mayor of Cleansburg, and there are three candidates for the position: Smith, Jones, and Brown. The day before the election a telephone poll of 680 randomly chosen registered voters produced the following results: 306 people surveyed indicated that they would vote for Smith, 272 indicated that they would vote for Jones and 102 indicated that they would vote for Brown. Do you think that the sampling error in this example was due primarily to sampling bias or to chance? Explain your answer

As part of a sixth-grade class project the teacher brings to class a large jar containing 200 gumballs of two different colors: red and green. Brianna is asked to draw a sample of her own choosing and estimate the number of red gumballs in the jar. Brianna draws a sample of 40 gumballs, of which 14 are red and 26 are green. Use Brianna's sample to estimate the number of red gumballs in the jar.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.