Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q3 (page 281)

Small Sample Data set 29 “Coin Weights” in Appendix B includes weights of 20 one-dollar coins. Given that the sample size is less than 30, what requirement must be met in order to treat the sample mean as a value from a normally distributed population? Identify three tools for verifying that requirement.

Short Answer

Expert verified

It is important to verify that the sample is from a population that follows a normal distribution.

The following three tools can be applied to check the normality of the data:

  • Construction of the histogram
  • Construction of the normal quantile plot
  • Identification of outliers

Step by step solution

01

Given information

A sample of weights of 20 one-dollar coins is considered.

02

Examining normality of the data

It is given that the sample of weights of one-dollar coins is considered.

The sample size is equal to 20, which is less than 30.

Since the sample size is less than 30, the sample cannot be considered a normally distributed population unless the distribution is examined/tested.

The requirement that must be fulfilled is that the sample observations must be from a normally distributed population.

The following three tools can be utilized to test whether the sample comes from a normally distributed population or not:

  • A histogram of the sample values can be plotted. The sample is from a normally distributed population if the histogram is approximately bell-shaped.
  • A normal quantile plot of the sample values can be plotted.The sample is from a normally distributed population if the plot consists of points that follow a straight-line pattern.
  • Outliers, if present, can be identified. If the number of outliers present is more than one, the sample is not from a normally distributed population.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Standard Normal DistributionIn Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Greater than 0.18

Births: Sampling Distribution of Sample Proportion For three births, assume that the genders are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from three births. Does the mean of the sample proportions equal the proportion of girls in three births? (Hint: See Exercise 15 for two births.)

Low Birth Weight The University of Maryland Medical Center considers “low birth weights” to be those that are less than 5.5 lb or 2495 g. Birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g (based on Data Set 4 “Births” in Appendix B).

a. If a birth weight is randomly selected, what is the probability that it is a “low birth weight”?

b. Find the weights considered to be significantly low, using the criterion of a birth weight having a probability of 0.05 or less.

c. Compare the results from parts (a) and (b).

Standard Normal DistributionIn Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers

to four decimal places.

Between -2.75 and -0.75.

Random Digits Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can the methods of this section be used to find the probability that when one digit is randomly generated, it is less than 3? Why or why not? What is the probability of getting a digit less than 3?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.

Sign-up for free