data & statistics homework 1

Bringing It Together: Homework

Seven hundred and seventy-one distance learning students at Long Beach City College responded to surveys in the 2010-11 academic year. Highlights of the summary report are listed in Table 1.39 .

• What percent of the students surveyed do not have a computer at home?
• About how many students in the survey live at least 16 miles from campus?
• If the same survey were done at Great Basin College in Elko, Nevada, do you think the percentages would be the same? Why?

Several online textbook retailers advertise that they have lower prices than on-campus bookstores. However, an important factor is whether the Internet retailers actually have the textbooks that students need in stock. Students need to be able to get textbooks promptly at the beginning of the college term. If the book is not available, then a student would not be able to get the textbook at all, or might get a delayed delivery if the book is back ordered.

A college newspaper reporter is investigating textbook availability at online retailers. He decides to investigate one textbook for each of the following seven subjects: calculus, biology, chemistry, physics, statistics, geology, and general engineering. He consults textbook industry sales data and selects the most popular nationally used textbook in each of these subjects. He visits websites for a random sample of major online textbook sellers and looks up each of these seven textbooks to see if they are available in stock for quick delivery through these retailers. Based on his investigation, he writes an article in which he draws conclusions about the overall availability of all college textbooks through online textbook retailers.

Write an analysis of his study that addresses the following issues: Is his sample representative of the population of all college textbooks? Explain why or why not. Describe some possible sources of bias in this study, and how it might affect the results of the study. Give some suggestions about what could be done to improve the study.

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Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction

• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Introductory Statistics
• Publication date: Sep 19, 2013
• Location: Houston, Texas
• Book URL: https://openstax.org/books/introductory-statistics/pages/1-introduction
• Section URL: https://openstax.org/books/introductory-statistics/pages/1-bringing-it-together-homework

© Jun 23, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

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1.E: Introduction to Statistics (Exercises)

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These are homework exercises to accompany the Textmap created for "Introductory Statistics" by Shafer and Zhang.

1.1: Basic Definitions and Concepts

Explain what is meant by the term population .

Explain what is meant by the term sample .

Explain how a sample differs from a population.

Explain what is meant by the term sample data .

Explain what a parameter is.

Explain what a statistic is.

Give an example of a population and two different characteristics that may be of interest.

Describe the difference between descriptive statistics and inferential statistics . Illustrate with an example.

Identify each of the following data sets as either a population or a sample:

• The grade point averages (GPAs) of all students at a college.
• The GPAs of a randomly selected group of students on a college campus.
• The ages of the nine Supreme Court Justices of the United States on \(\text{January}\; 1,\; 1842\).
• The gender of every second customer who enters a movie theater.
• The lengths of Atlantic croakers caught on a fishing trip to the beach.

Identify the following measures as either quantitative or qualitative:

• The \(30\) high-temperature readings of the last \(30\) days.
• The scores of \(40\) students on an English test.
• The blood types of \(120\) teachers in a middle school.
• The last four digits of social security numbers of all students in a class.
• The numbers on the jerseys of \(53\) football players on a team.
• The genders of the first \(40\) newborns in a hospital one year.
• The natural hair color of \(20\) randomly selected fashion models.
• The ages of \(20\) randomly selected fashion models.
• The fuel economy in miles per gallon of \(20\) new cars purchased last month.
• The political affiliation of \(500\) randomly selected voters.

A researcher wishes to estimate the average amount spent per person by visitors to a theme park. He takes a random sample of forty visitors and obtains an average of \(\$28\) per person.

• What is the population of interest?
• What is the parameter of interest?
• Based on this sample, do we know the average amount spent per person by visitors to the park? Explain fully.

A researcher wishes to estimate the average weight of newborns in South America in the last five years. He takes a random sample of \(235\) newborns and obtains an average of \(3.27\) kilograms.

• Based on this sample, do we know the average weight of newborns in South America? Explain fully.

A researcher wishes to estimate the proportion of all adults who own a cell phone. He takes a random sample of \(1,572\) adults; \(1,298\) of them own a cell phone, hence \(1298/1572 \approx 0.83\) or about \(83\%\) own a cell phone.

• What is the statistic involved?
• Based on this sample, do we know the proportion of all adults who own a cell phone? Explain fully.

A sociologist wishes to estimate the proportion of all adults in a certain region who have never married. In a random sample of \(1,320\) adults, \(145\) have never married, hence \(145/1320 \approx 0.11\) or about \(11\%\) have never married.

• Based on this sample, do we know the proportion of all adults who have never married? Explain fully.
• What must be true of a sample if it is to give a reliable estimate of the value of a particular population parameter?
• What must be true of a sample if it is to give certain knowledge of the value of a particular population parameter?
• A population is the total collection of objects that are of interest in a statistical study.
• A sample, being a subset, is typically smaller than the population. In a statistical study, all elements of a sample are available for observation, which is not typically the case for a population.
• A parameter is a value describing a characteristic of a population. In a statistical study the value of a parameter is typically unknown.
• All currently registered students at a particular college form a population. Two population characteristics of interest could be the average GPA and the proportion of students over \(23\) years.
• Population.
• Qualitative.
• Quantitative.
• All newborn babies in South America in the last five years.
• The average birth weight of all newborn babies in South America in the last five years.
• No, not exactly, but we know the approximate value of the average.
• All adults in the region.
• The proportion of the adults in the region who have never married.
• The proportion computed from the sample, \(0.1\).
• No, not exactly, but we know the approximate value of the proportion.

1.2: Overview

1.3: presentation of data.

1. List all the measurements for the data set represented by the following data frequency table.

\[\begin{array}{c|ccccc}x & 31 & 32 & 33 & 34 & 35 \\ \hline f & 1 & 5 & 6 & 4 & 2\end{array}\]

2. List all the measurements for the data set represented by the following data frequency table

\[\begin{array}{c|ccccccc}x & 97 & 98 & 99 & 100 & 101 & 102 & 103 & 105 \\ \hline f & 7 & 5 & 3 & 4 & 2 & 2 & 1 & 1\end{array}\]

3. Construct the data frequency table for the following data set.

\[\begin{array}22 & 25 & 22 & 27 & 24 & 23 \\ 26 & 24 & 22 & 24 & 26 &\end{array}\]

4. Construct the data frequency table for the following data set.

\[ \{1,\, 5,\, 2,\, 3,\, 5,\, 1,\, 4,\, 4,\, 4,\, 3,\, 2,\, 5,\, 1,\, 3,\, 2,\, 1,\, 1,\, 1,\, 2\} \]

• \(\{31,\, 32,\, 32,\, 32,\, 32,\, 32,\, 33,\, 33,\, 33,\, 33,\, 33,\, 33,\, 34,\, 34,\, 34,\, 34,\, 35,\, 35\}\)
• \(\begin{array}{c|ccccc}x & 22 & 23 & 24 & 25 & 26 & 27 \\ \hline f & 3 & 1 & 3 & 1 & 2 & 1\end{array}\)

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