/*! 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 15 During the previous calendar yea... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 15

During the previous calendar year, a county's small claims court processed 870 cases. Describe how a simple random sample of size \(n=50\) might be selected from the case files to obtain information regarding the average award in such cases.

Short Answer

Expert verified
Assign unique numbers to each case and randomly generate 50 numbers between 1 and 870. Select the cases corresponding to the randomly generated numbers to form your sample. From this random sample, you can calculate statistical data like the average award.

Step by step solution

01

Number the cases

First, assign each of the 870 cases a unique number from 1 to 870. This is necessary for maintaining an organized selection of cases for the random sample.
02

Use a random number generator

Next, using an appropriate tool such a random number generator, generate 50 random numbers between 1 and 870. Ensure these numbers are not repeated. Use a computer program or statistical software to do this task.
03

Select the cases

Finally, select the cases based on the generated random numbers and use them to form the sample of size \(n=50\). This forms the random sample from the population of cases. From this sample, statistical analysis such as calculation of the average award can be conducted.

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.

Random Number Generator
A Random Number Generator (RNG) is an essential tool in the process of creating a simple random sample. This tool generates a sequence of numbers that lack any discernible pattern, effectively simulating the randomness akin to drawing lots from a hat.

In our county's small claims court, an RNG would randomly select numbers assigned to case files.
  • Each case must be numbered from 1 to 870.
  • The RNG will select 50 random numbers from this range.
  • The primary goal here is to ensure each case has an equal chance of being chosen.

Using computer programs and statistical software like Excel or Python's random module simplifies this task. By ensuring numbers aren't repeated, the sample maintains its randomness, providing a true reflection of the population.

Random number generators help eliminate biases, which is crucial for the reliability of statistical conclusions drawn from the sample.
Population and Sample
In any statistical study, understanding the population and sample is fundamental. The population refers to the entire group about which we want to draw conclusions. In our scenario with the small claims court, the population comprises all 870 cases from the past year.

On the other hand, a sample is a smaller subset, selected from this larger group.
  • The sample size here is 50 cases.
  • By selecting a sample, researchers can gather insights without examining every single case.

Using a representative sample allows for efficient analysis, saving both time and resources. This method is often used when it鈥檚 impractical to study the whole population. The key is to ensure the sample accurately reflects the population to make valid inferences.
Statistical Analysis
Once a simple random sample is obtained, statistical analysis can commence. This process involves examining the data gathered from the sample to understand trends, patterns, or insights about the larger population.

In the context of our small claims court cases, one might want to calculate the average award given. Calculating this average from the sample serves as an estimate of the average in the entire population of cases.
  • Begin by adding all award amounts from the sampled cases.
  • Then, divide this total by the number of cases in the sample, which is 50 in this situation.
  • The result provides an estimate of the average award for all small claims processed.

Statistical analysis goes beyond just the mean, allowing for further exploration of variability, median values, and potential outliers within the sample. This scientific approach ensures decisions and conclusions made are backed by data rather than assumptions.

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

An experiment was carried out to assess the effect of Sweet Talk, a text messaging support system for patients with diabetes ("A Randomized Controlled Trial of Sweet Talk," Diabetic Medicine \([2 \mathrm{OO} 6]: 1332-1338) .\) Participants in the experiment were 92 patients, age 8 to \(18,\) with type I diabetes who had been on conventional insulin treatment for at least one year. Participants were assigned at random to one of three experimental groups: Group 1: continued conventional insulin therapy Group 2: continued conventional insulin therapy with Sweet Talk support Group 3: followed a new intensive insulin therapy with Sweet Talk support One response variable was a measure of glucose concentration in the blood. There was no significant difference in glucose concentration between groups 1 and \(2,\) but group 3 showed a significant improvement in this measure compared to groups 1 and 2 . a. Explain why it is not reasonable to attribute the observed improvement in group 3 compared to group 1 to the use of Sweet Talk, even though subjects were randomly assigned to the three experimental groups. b. How would you modify this experiment so that you could tell if improvement in glucose concentration was attributable to the intensive insulin therapy, the use of Sweet Talk, or a combination of the two? c. Draw a diagram showing the structure of the modified experiment from Part (b).

Can choosing the right music make wine taste better? This question was investigated by a researcher at a university in Edinburgh (www. decanter.com/news). Each of 250 volunteers was assigned at random to one of five rooms where they were asked to taste and rate a glass of wine. In one of the rooms, no music was playing and a different style of music was playing in each of the other four rooms. The researchers concluded that cabernet sauvignon is perceived as being richer and more robust when bold music is played than when no music is heard. a. Is the study described an observational study or an experiment? b. Can a case be made for the researcher's conclusion that the music played was the cause for the higher rating? Explain.

The article "High Levels of Mercury Are Found in Californians" (Los Angeles Times, February \(9,2 \mathrm{OO} 6\) ) describes a study in which hair samples were tested for mercury. The hair samples were obtained from more than 6000 people who voluntarily sent hair samples to researchers at Greenpeace and The Sierra Club. The researchers found that nearly one-third of those tested had mercury levels that exceeded the concentration thought to be safe. Is it reasonable to generalize this result to the larger population of U.S. adults? Explain why or why not.

Explain why some studies include both a control group and a placebo treatment. What additional comparisons are possible if both a control group and a placebo group are included?

Researchers at the Hospital for Sick Children in Toronto compared babies born to mothers with diabetes to babies born to mothers without diabetes ("Conditioning and Hyperanalgesia in Newborns Exposed to Repeated Heel Lances," Journal of the American Medical Association [2002]: \(857-861\) ). Babies born to mothers with diabetes have their heels pricked numerous times during the first 36 hours of life in order to obtain blood samples to monitor blood sugar level. The researchers noted that the babies born to diabetic mothers were more likely to grimace or cry when having blood drawn than the babies born to mothers without diabetes. This led the researchers to conclude that babies who experience pain early in life become highly sensitive to pain. Comment on the appropriateness of this conclusion.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.