Statistics: Sampling and Variables

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Questions and Answers

Briefly describe the two meanings of the word statistics.

Statistics can refer to numerical data or to the field of study dealing with the collection, analysis, interpretation, presentation, and organization of data.

Identify three main differences between statistics and probability.

Statistics involves making inferences from data, dealing with uncertainty and variability, and using data to make predictions and decisions, whereas probability is the branch of mathematics that deals with quantifying uncertainty and calculating the likelihood of events.

In each statement, decide whether descriptive or inferential statistics is used. Based on Mrs. Smith's electric bill for last year she expects that she will be paying $75/month this year.

  • Descriptive statistics
  • Inferential statistics (correct)

In each statement, decide whether descriptive or inferential statistics is used. The amount of time needed to run the Suva marathon is more than 3 hours.

<p>Descriptive statistics (B)</p> Signup and view all the answers

In each statement, decide whether descriptive or inferential statistics is used. Next year, the sea level will be higher than now.

<p>Inferential statistics (B)</p> Signup and view all the answers

Explain whether each of the following constitutes a population or a sample. Weight of 30 students in ST130 course.

<p>Sample, because it is a subset of all students in the ST130 course.</p> Signup and view all the answers

Explain whether each of the following constitutes a population or a sample. Time span to wait for all customers to be served in a Southern Cross restaurant.

<p>Population, because it refers to all customers served in the restaurant.</p> Signup and view all the answers

Explain whether each of the following constitutes a population or a sample. Yield of taro per acre for 10 pieces of land.

<p>Sample, because it is a subset of all pieces of land.</p> Signup and view all the answers

Explain whether each of the following constitutes a population or a sample. Cows owned by all dairy farmers in Ba.

<p>Population, because it encompasses all cows owned by dairy farmers in Ba.</p> Signup and view all the answers

Which sampling method is used in each case? Interviewing every 14th customer leaving a theatre about the movie they had seen.

<p>Systematic sampling</p> Signup and view all the answers

Which sampling method is used in each case? The country is divided into economic classes and a sample is chosen from each class to be surveyed.

<p>Stratified sampling</p> Signup and view all the answers

Which sampling method is used in each case? A researcher divided subjects into 4 geographical groups and then selected all members from a randomly selected group as samples.

<p>Cluster sampling</p> Signup and view all the answers

Which sampling method is used in each case? A Math's tutor at USP is interested in the mean number of days an ST130 student is absent from tutorial classes. The tutor takes her sample by gathering data on 5 randomly selected students from ST130 course.

<p>Random sampling</p> Signup and view all the answers

When running an experimental study, the group that is manipulated can be called the independent group.

<p>False (B)</p> Signup and view all the answers

Define the relationship between confounding, dependent, and independent variables?

<p>Independent variables are manipulated by researchers. Dependent variables are measured to see how they are affected by the independent variable. Confounding variables are extraneous variables that can affect the dependent variable.</p> Signup and view all the answers

Explain the difference between qualitative, quantitative, discrete, and continuous variables, then classify each variable as qualitative nominal, qualitative ordinal or quantitative discrete or quantitative continuous. Number of apples sold in Suva market every one hour.

<p>Quantitative Discrete</p> Signup and view all the answers

Explain the difference between qualitative, quantitative, discrete, and continuous variables, then classify each variable as qualitative nominal, qualitative ordinal or quantitative discrete or quantitative continuous. Ranking of tennis players.

<p>Qualitative Ordinal</p> Signup and view all the answers

Explain the difference between qualitative, quantitative, discrete, and continuous variables, then classify each variable as qualitative nominal, qualitative ordinal or quantitative discrete or quantitative continuous. Time it takes to cut the lawn.

<p>Quantitative Continuous</p> Signup and view all the answers

Explain the difference between qualitative, quantitative, discrete, and continuous variables, then classify each variable as qualitative nominal, qualitative ordinal or quantitative discrete or quantitative continuous. Classification of children in a day care center as infant, toddler, preschool.

<p>Qualitative Ordinal</p> Signup and view all the answers

Classify each as nominal-level, ordinal-level, interval-level or ratio-level measurement. Temperatures inside 10 fridges (in degrees Celsius).

<p>Interval-level</p> Signup and view all the answers

Classify each as nominal-level, ordinal-level, interval-level or ratio-level measurement. Level of performance (poor, fair, good, excellent).

<p>Ordinal-level</p> Signup and view all the answers

Classify each as nominal-level, ordinal-level, interval-level or ratio-level measurement. Categories of magazines in a physician's office (sports, women's, health, men's, news).

<p>Nominal-level</p> Signup and view all the answers

Classify each as nominal-level, ordinal-level, interval-level or ratio-level measurement. Times required by a student to complete the ST130 test.

<p>Ratio-level</p> Signup and view all the answers

Name and define two areas of statistics.

<p>Descriptive statistics, which involves summarizing and presenting data, and inferential statistics, which involves making predictions or generalizations based on a sample.</p> Signup and view all the answers

What is probability? Name two areas where probability is used.

<p>Probability is the measure of the likelihood that an event will occur. Two areas where probability is used are weather forecasting and insurance risk assessment.</p> Signup and view all the answers

Suggest some ways that statistics can be used in everyday life.

<p>Tracking personal finances, monitoring health metrics, and making informed purchasing decisions.</p> Signup and view all the answers

Explain the differences between a sample and a population.

<p>A population is the entire group of individuals or items of interest, while a sample is a subset of the population selected for study.</p> Signup and view all the answers

Why are samples used in statistics?

<p>Samples are used because it is often impractical or impossible to study the entire population.</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. In the year 2010, 148 million Americans will be enrolled in HMO.

<p>Descriptive statistics (B)</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. Nine out of ten on-the-job fatalities are men.

<p>Descriptive statistics (B)</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. Expenditures in the cable industry were $5.66 billion in 1996.

<p>Descriptive statistics (B)</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. The median Household income for people aged 24-35 is $35,888.

<p>Descriptive statistics (A)</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. Allergy therapy makes bees go away.

<p>Inferential statistics (A)</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. Drinking decaffeinated coffee can raise cholesterol levels by 7%.

<p>Inferential statistics (B)</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. The national average annual medicine expenditure per person is $1052.

<p>Descriptive statistics (A)</p> Signup and view all the answers

In each of the statements, tell whether descriptive or inferential statistics have been used. Experts say that mortgage rates may soon hit bottom.

<p>Inferential statistics (A)</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. pages in the city of Cleveland telephone book.

<p>Ratio-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Rankings of tennis players.

<p>Ordinal-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Weights of air conditioners.

<p>Ratio-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Temperatures inside 10 refrigerators.

<p>Interval-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Salaries of the top 5 CEOs in the United States.

<p>Ratio-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Rating of eight local plays (poor, fair, good, excellent).

<p>Ordinal-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Times required for mechanics to do a tune-up.

<p>Ratio-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Age of students in a classroom.

<p>Ratio-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Marital status of patients in a physician's office.

<p>Nominal-level</p> Signup and view all the answers

Classify each as nominal-level, ordinary-level, interval-level, or ratio-level measurement. Horsepower of tractor engines.

<p>Ratio-level</p> Signup and view all the answers

Classify each variable as qualitative or quantitative. Number of bicycles sold in 1 year by a large sporting goods store.

<p>Quantitative</p> Signup and view all the answers

Classify each variable as qualitative or quantitative. Colors of baseball caps in a store.

<p>Qualitative</p> Signup and view all the answers

Classify each variable as qualitative or quantitative. Time it takes to cut down a lawn.

<p>Quantitative</p> Signup and view all the answers

Classify each variable as qualitative or quantitative. Capacity in cubic feet of six truck beds.

<p>Quantitative</p> Signup and view all the answers

Classify each variable as qualitative or quantitative. Classification of children in a day-care center (infant, toddler, preschool).

<p>Qualitative</p> Signup and view all the answers

Classify each variable as qualitative or quantitative. Weights of fish caught in Lake George.

<p>Quantitative</p> Signup and view all the answers

Classify each variable as qualitative or quantitative. Marital status of faculty members in a large university.

<p>Qualitative</p> Signup and view all the answers

Classify each variable as discrete or continuous. number of doughnuts sold each day by Doughnut Heaven.

<p>Discrete</p> Signup and view all the answers

Classify each variable as discrete or continuous. Water temperature of six swimming pools in Pittsburg on a given day.

<p>Continuous</p> Signup and view all the answers

Classify each variable as discrete or continuous. Weights of cats in a pet shelter.

<p>Continuous</p> Signup and view all the answers

Classify each variable as discrete or continuous. Lifetime (in hours) of 12 flashlight batteries.

<p>Continuous</p> Signup and view all the answers

Classify each variable as discrete or continuous. Number of cheeseburgers sold each day by a hamburger stand on a college campus.

<p>Discrete</p> Signup and view all the answers

Classify each variable as discrete or continuous. Number of DVDs rented each day by a video store.

<p>Discrete</p> Signup and view all the answers

Classify each variable as discrete or continuous. Capacity (in gallons) of six reservoirs in Jefferson County.

<p>Continuous</p> Signup and view all the answers

Classify each sample as random, systematic, stratified, or cluster. In a large school district, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in previous years.

<p>Cluster</p> Signup and view all the answers

Classify each sample as random, systematic, stratified, or cluster. Every seventh customer entering a shopping mall is asked to select his or her favorite store

<p>Systematic</p> Signup and view all the answers

Classify each sample as random, systematic, stratified, or cluster. Nursing supervisors are selected using random number in order to determine annual salaries.

<p>Random</p> Signup and view all the answers

Classify each sample as random, systematic, stratified, or cluster. Every 110th hamburger manufactured is checked to determine its fat content.

<p>Systematic</p> Signup and view all the answers

Classify each sample as random, systematic, stratified, or cluster. Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from each group and interviewed to determine whether they have been bitten by a dog last year.

<p>Stratified</p> Signup and view all the answers

Identify each study as being either observational or experimental. Subjects were randomly assigned to two groups, and one group was given an herb and other group a placebo. After 6 months, the number of respiratory tract infections each group had was compared.

<p>Experimental</p> Signup and view all the answers

Identify each study as being either observational or experimental. A researcher stood at a busy intersection to see if colour of an automobile that person drives is related to running red lights.

<p>Observational</p> Signup and view all the answers

Identify each study as being either observational or experimental. A researcher finds that people who are more hostile have higher total cholesterol levels than those who are less hostile.

<p>Observational</p> Signup and view all the answers

Identify each study as being either observational or experimental. Subjects are randomly assigned to four groups. Each group is placed on one of four special diets-a low-fat diet, a high-fish diet, a combination of low-fat diet and high-fish diet, and a regular diet. After 6 months, the blood pressures of the groups are compared to see if diet has any affect on blood pressure.

<p>Experimental</p> Signup and view all the answers

Briefly identify a member, a variable, an observation, and a data set with reference to this table.

<p>Member: Suva, Variable: Amount of rainfall, Observation: 57, Data set: All the amounts of rainfall for each place.</p> Signup and view all the answers

Briefly explain the difference between sampling with replacement and sampling without replacement.

<p>In sampling with replacement, each selected item is returned to the population before the next selection, allowing it to be selected again. In sampling without replacement, selected items are not returned to the population, so they cannot be selected again.</p> Signup and view all the answers

Briefly explain the difference between the terms statistic and parameter.

<p>A parameter is a numerical value that describes a characteristic of the entire population, while a statistic is a numerical value that describes a characteristic of a sample.</p> Signup and view all the answers

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 ≈ .11 or about 11% have never married. What is the population of interest?

<p>All adults in the certain region.</p> Signup and view all the answers

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 ≈ .11 or about 11% have never married. What is the parameter of interest?

<p>The proportion of all adults in that region who have never married.</p> Signup and view all the answers

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 ≈ .11 or about 11% have never married. What is the statistic involved?

<p>The sample proportion of adults who have never married, which is 145/1320 ≈ 0.11.</p> Signup and view all the answers

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 ≈ .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.

<p>No, we do not know the exact proportion. The sample proportion (0.11) is an estimate, but there will be sampling error. Confidence intervals can provide a range within which the true proportion likely falls.</p> Signup and view all the answers

Flashcards

Descriptive vs. Inferential Statistics

Descriptive statistics organizes and summarizes data, while inferential statistics uses sample data to make predictions about a population.

Population vs. Sample

A population includes all members of a specified group, while a sample is a subset of the population.

Qualitative vs. Quantitative Variables

A qualitative variable describes qualities or characteristics, while a quantitative variable measures numerical data.

Levels of Measurement

Nominal: categories with no order. Ordinal: categories with a meaningful order. Interval: equal intervals, no true zero. Ratio: true zero point.

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Discrete vs. Continuous Variables

Discrete variables are countable and finite, while continuous variables can take on any value within a range.

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Sampling Methods

Random sampling ensures every member has an equal chance. Systematic sampling selects every nth member. Stratified sampling divides into subgroups then samples. Cluster sampling divides into clusters, samples all in selected clusters.

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Observational vs. Experimental Studies

An observational study watches and records. An experimental study manipulates variables to determine effect.

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Sampling with/without Replacement

Sampling with replacement allows the same item to be selected again, while sampling without replacement does not.

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Statistic vs. Parameter

A statistic describes a sample, while a parameter describes a population.

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Independent, Dependent, Confounding Variables

The independent variable is what you manipulate; the dependent variable is what you measure; confounding variables are extraneous factors.

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Study Notes

  • Statistics has two meanings: numerical facts and the field of study dealing with data.
  • Statistics and probability differ in focus and application.
  • Descriptive statistics summarizes data, while inferential statistics makes predictions.
  • Population refers to the entire group, while a sample is a subset of the population.

Sampling Methods

  • Systematic sampling involves selecting every nth member.
  • Stratified sampling divides the population into subgroups and samples from each.
  • Cluster sampling involves selecting entire groups or clusters.

Experimental Studies

  • The manipulated group in an experimental study is called the independent group.

Variables

  • Qualitative variables are categorical, while quantitative variables are numerical.
  • Discrete variables are countable, and continuous variables can take any value within a range.
  • Nominal variables are categorical with no order, ordinal variables have a meaningful order.
  • Interval variables have equal intervals but no true zero point.
  • Ratio variables have a true zero point.

Levels of Measurement

  • Nominal-level: Categories with no inherent order
  • Ordinal-level: Categories with a meaningful order
  • Interval-level: Equal intervals, no true zero
  • Ratio-level: True zero point

Study Types

  • Observational studies observe characteristics without intervention.
  • Experimental studies involve manipulating variables.

Sampling with/without Replacement

  • Sampling with replacement allows the same unit to be selected multiple times.
  • Sampling without replacement does not.

Statistics vs. Parameters

  • A statistic is a value calculated from a sample.
  • A parameter is a value that represents the truth about the population.

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