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Chapter 3: Problem 12

Which sampling method is being described? a. In a study, the sample is chosen by separating all cars by size and selecting 10 of each size grouping. b. In a study, the sample is chosen by writing everyone's name on a playing card, shuffling the deck, then choosing the top 20 cards. c. Every 4th person on the class roster was selected.

Short Answer

Expert verified
a. Stratified Sampling b. Simple Random Sampling c. Systematic Sampling

Step by step solution

01

Identifying the Method in Part a

In part a, the study describes dividing the population (cars) into distinct groups based on a characteristic (size) and then taking a sample of 10 from each group. This method of sampling is called 'Stratified Sampling'. Here, the population is divided into strata (groups), and a sample is drawn from each stratum.
02

Identifying the Method in Part b

For part b, the study describes writing each individual's name on a card, shuffling, and selecting from the top. This method is characteristic of 'Simple Random Sampling'. In simple random sampling, every individual from the population has an equal chance of being selected, which is achieved by random shuffling and drawing.
03

Identifying the Method in Part c

In part c, the sample is chosen by selecting every 4th person from a list (class roster). This method is known as 'Systematic Sampling'. Systematic sampling involves selecting every nth item from a larger set, which makes it systematic by following a certain pattern.

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Key Concepts

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

Stratified Sampling
In stratified sampling, the population is divided into distinct subgroups known as strata. Each stratum is made up of individuals that share a specific characteristic. For example, if you are studying something about a population of cars, you might create strata based on sizes such as small, medium, and large.

Once the population is divided into these groups, or strata, a sample is taken from each. This might mean selecting a certain number of individuals from each stratum to ensure representation from the entire population. This sampling method is beneficial when the population has diverse segments that are expected to differ in the outcome of interest.
  • Ensures representation: Stratified sampling aims to represent all important subgroups within a population.
  • Useful for heterogeneous populations: When a population is diverse with respect to important characteristics, this method is very effective.
  • Reduces sampling error: Providing balanced representation of different strata helps in reducing the sampling error.
Simple Random Sampling
Simple random sampling is a straightforward sampling technique where each member of the population has an equal probability of being selected. Imagine you have a deck of cards where each card represents a member of the population. You shuffle the cards well, and the chosen top cards form your sample. This method guarantees that every individual has the same chance to be selected.

This strategy is easy to implement and requires minimal knowledge about the population. Since every member has an equal chance of selection, it ensures unbiasedness and simplicity.
  • Equal chance: Every member of the population can be selected.
  • Easy to conduct: As long as you can randomly select individuals, it is simple to implement.
  • Unbiased: Randomizing the selection process avoids bias.
Systematic Sampling
Systematic sampling involves selecting every nth individual from a list after randomly determining a starting point. You might start with the 3rd individual on a list and then pick every 4th one thereafter. This creates a systematic inclusion of samples within a study, making it distinct from simply random choices.

This method is straightforward to execute especially when working with ordered lists, such as a class roster or directory. It can be efficient and is favored when a complete list of the population is accessible.
  • Easy to execute: Once the starting point and interval (n) are defined, the process is simple.
  • Efficient for ordered populations: Especially useful when working with organized data like lists.
  • Potential for periodicity: Be mindful of patterns within data that might coincide with the interval, as it may skew results.

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Most popular questions from this chapter

Identify the sampling method. Just the name will suffice. a. Researchers select every 5 th customer who walks into the store to take a survey. b. Raffle tickets are distributed and collected in a bag, where they are mixed and ten are drawn for prizes. c. I asked the shoppers near me in the shoe department what size they wear. d. An IRS auditor randomly selects 25 taxpayers in each filing status (single, head of household, married filing jointly, and married filing separately).

You recorded the time in seconds it took for 8 participants to solve a puzzle. The times were: 15.2,18.8 , 19.3,19.7,20.2,21.8,22.1,29.4 a. Find the mean, including units. b. Find the median, including units. c. Based on the mean and the median, would you expect the distribution to be symmetric, skewed left, or skewed right? Explain.

Portland Community College serves nearly 73,000 full-time and part-time students in the greater Portland area at four main campuses (SE, Cascade, Sylvania, and \(\mathrm{RC}\) ). Student Affairs would like to know how students get to campus. They randomly select 250 students from each of the four main campus and ask them how they got to classes on campus. The following are the results of their survey: \- Public Transportation: 435 \- Driving: 475 \- Biking: 65 \- Walking: 30 a. Identify the population and state its size. b. Identify the sample and state its size. c. What sampling method was used? d. What type of data was collected? e. Give the statistic for the percentage of students who use public transportation.

Use the Empirical Rule to answer these questions. About what percentage of the values from a Normal distribution fall between the first and third standard deviations (both sides)?

True or False: The bars of a bar graph should always touch.
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