/*! 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 22 A hotel has 30 floors with 40 ro... [FREE SOLUTION] | 91影视

91影视

A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to survey 120 guests who stayed at the hotel during a convention about their overall satisfaction with the property. (a) Explain why choosing a stratified random sample might be preferable to an SRS in this case. What would you use as strata? (b) Why might a cluster sample be a simpler option? What would you use as clusters?

Short Answer

Expert verified
Stratified sampling ensures room type representation; cluster sampling is simpler by using whole floors as clusters.

Step by step solution

01

Understanding Stratified Sampling

In stratified sampling, the population is divided into strata, groups that share similar characteristics, and a random sample is taken from each stratum. This approach is ideal when researchers suspect that certain subgroups within a population may have similar responses, and they want each subgroup to be represented accurately in the sample.
02

Analyzing SRS Limitations

In a simple random sample (SRS), every individual has an equal chance of being selected. Although this is straightforward, it does not guarantee that different subgroups (e.g., guests with different room views) are proportionally represented.
03

Identifying Strata for Sampling

In this hotel scenario, room view is a key factor that might affect guest satisfaction. Therefore, the rooms facing the water can be one stratum, and the rooms facing the golf course can be another. Stratified sampling ensures that guests from both types of rooms are represented proportionally in the survey.
04

Advantages of Stratified Sampling

Stratified sampling ensures that specific subsegments, such as guests in water-view rooms and golf-course-view rooms, are represented. This can highlight differences or similarities in satisfaction levels across room types, which might be relevant to the hotel's management.
05

Introduction to Cluster Sampling

Cluster sampling involves dividing the population into clusters and then randomly selecting entire clusters. This can simplify logistics, especially when the population is large and dispersed.
06

Clusters in the Hotel Context

In the case of the hotel, each floor could serve as a cluster, as it contains a mix of both room types. Instead of sampling guests from all floors, a few floors (clusters) could be selected entirely for the survey.
07

Advantages of Cluster Sampling

Cluster sampling is simpler and more cost-effective in scenarios where the population is naturally divided. For the hotel, it minimizes efforts because surveying all guests on a few selected floors is easier than reaching guests from all 30 floors.

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.

Stratified Sampling
Stratified sampling is a method used to ensure that specific subgroups within a population are represented in a sample. In the case of the hotel, this approach is quite beneficial. Each type of room view 鈥 water view and golf course view 鈥 can be considered separate strata. By dividing the guests into these groups, the hotel manager can ensure that feedback is accurately gathered from both sides, reflecting any possible differences in satisfaction.

This approach is particularly useful when certain characteristics, like room views, are likely to influence the outcome, which in this case is the satisfaction level. A stratified sample seeks to capture these variances by sampling within each subgroup, ensuring an accurate representation in the feedback. By doing this, the hotel can better understand if there's a significant difference in satisfaction levels between guests with different room views. This information can help in decision-making and improving guest services.
Cluster Sampling
Cluster sampling offers a simpler, often more cost-effective, method when dealing with a large and dispersed population. In this hotel scenario, each floor acts as a natural cluster since it contains both types of room views. Instead of sampling guests from every floor, the manager might decide to randomly select one or several floors and survey all guests on those floors.

Cluster sampling reduces the complexity of the survey process. It minimizes the logistical challenges because fewer locations are selected for sampling. Although this method might not capture as diverse opinions as a stratified approach, it is efficient and straightforward to implement. This method is particularly handy when time and budget constraints are in place.
Simple Random Sampling (SRS)
Simple random sampling (SRS) is a straightforward technique where each individual has an equal chance of being selected for the survey. It is easy to understand and implement, but in this hotel case, it may not be the most effective method.

With SRS, there's no guarantee that guests from rooms with different views are proportionally represented. This can lead to biased results if one group, such as guests with a water view, is more satisfied or dissatisfied than others. While SRS ensures fairness in selection, it doesn't account for distinct characteristics that might influence guest satisfaction, like the difference in room views. As a result, stratified or cluster sampling might be preferred when you need to highlight differences in responses between subgroups within the population.

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

A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 45,000 people made credit card purchases. Surveys are mailed to 1000 of these people, chosen at random, and 137 people return the survey form. Identify the population and the sample.

Canada requires that cars be equipped with 鈥渄aytime running lights,鈥 headlights that automatically come on at a low level when the car is started. Some manufacturers are now equipping cars sold in the United States with running lights. Will running lights reduce accidents by making cars more visible? An experiment conducted in a driving simulator suggests that the answer may be 鈥淵es.鈥 What concerns would you have about generalizing the results of such an experiment?

Fizz Laboratories, a pharmaceutical company, has developed a new drug for relieving chronic pain. Sixty patients suffering from arthritis and needing pain relief are available. Each patient will be treated and asked an hour later, 鈥淎bout what percent of pain relief did you experience?鈥 (a) Why should Fizz not simply administer the new drug and record the patients鈥 responses? (b) Should the patients be told whether they are getting the new drug or a placebo? How would this knowledge probably affect their reactions?

A double-blind experiment was conducted to evaluate the effectiveness of the Salk polio vaccine. The purpose of keeping the diagnosing physicians unaware of the treatment status of the experimental subjects was to (a) eliminate grounds for malpractice suits. (b) ensure that subjects were randomly assigned to treatments. (c) eliminate a possible source of bias. (d) make sure nobody is harmed. (e) avoid the placebo effect.

In using Table D repeatedly to choose random samples, you should not always begin at the same place, such as line 101. Why not?

See all solutions

Recommended explanations on Math Textbooks

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.