Chapter 1.2

How do you use simple random sampling?

- Any group of n individuals is equally likely to be chosen as any other group of n individuals - Each sample of the same size has an equal chance of being selected

How do you use convenience sampling?

- a type of sampling that is not random and involves using a population that is readily available - A related term is quota sampling: using a sample that is selected to match the population with respect to some specific characteristic(s)

How do you do systematic sampling?

-Randomly select a starting point in a list of names and take every nth piece of data from a listing of the population - Systematic sampling is a special subset of cluster sampling

Explain simple random sampling?

Any group of n individuals is equally likely to be chosen as any other group of n individuals

Jennifer wants to estimate the men amount of money spent on clothes per week by mall shoppers. She collects data from every 10th person entering one clothing store at the mall. Biased or Unbiased?

Biased

Kenneth wants to estimate the mean height of students at his school. He collects data by selecting a random group of students within his classroom. Biased or Unbiased?

Biased

Ruth wants to estimate the mean height of students at her school. She collects data by selecting a random group of students within her classroom. Biased or Unbiased?

Biased

To estimate the mean number of calories consumed by students at her school, Mary collects data from randomly selected individuals in the cafeteria for breakfast. Biased or Non-biased?

Biased

To estimate the political party distribution of residents in his state, Patrick collects data from a large group of randomly selected residents of his city. Biased or Unbiased?

Biased

To estimate which presidential candidate is likely to win the vote of a town, Mark collects data by interviewing people leaving a local Christian church. Biased or Unbiased?

Biased

A pollster interviews all human resource personnel in five different high tech companies. What type of sampling is used?

Cluster

The freshman, sophomore, junior, and senior years are numbered one, two, three, and four, respectively. A random generator is used to pick two of those years. All students in those two years are in the sample. What type of sampling is used?

Cluster

A student interviews classmates in his algebra class to determine how many pairs of jeans a student owns, on the average. What type of sampling is used?

Convenience

An administrative assistant is asked to stand in front of the library one Wednesday and to ask the first 100 undergraduate students he encounters what they paid for tuition in the Fall semester. Those 100 students are the sample. What type of sampling is used?

Convenience

How do you do cluster sampling?

Divide the population into groups, and then randomly select some of the groups

A sampling error is the situation in which not all members of the population are equally likely to be selected. True or False

False

Christopher wants to estimate the male to female ratio of the residents of his city. He collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents. Biased or Non-biased?

Non-biased

Ruby wants to estimate the mean grade point average of students at her school. She collects data by recording the grade point average of every 25th student on the list of students after a randomly selected first student. Biased or Non-biased?

Non-biased

To estimate the mean salary of professors at his university; Benjamin collects data by recording the salaries of all professors included in 12 randomly selected departments. Biased or Non-biased?

Non-biased

A completely random method is used to select 75 students. Each undergraduate student in the fall semester has the same probability of being chosen at any stage of the sampling process. What type of sampling is used?

Simple Random

A high school counselor uses a computer to generate 50 random numbers and then picks students whose names correspond to the numbers. What type of sampling is used?

Simple Random

A high school educational researcher interviews 50 high school female teachers and 50 high school male teachers. What type of sampling is used?

Stratified

A sample of 100 undergraduate San Jose State students is taken by organizing the students' names by classification (freshman, sophomore, junior, or senior), and them selecting 25 students from each. What type of sampling is used?

Stratified

A soccer coach selects six players from a group of boys aged eight to ten, seven players from a group of boys aged 11 to 12, and three players from a group of boys aged 13 to 14 to form a recreational soccer team. What type of sampling is used?

Stratified

A medical researcher interviews every third cancer patient from a list on cancer patients in the local hospital. What type of sampling is used?

Systematic

A random number generator is used to select a student from the alphabetical listing of all undergraduate students in the Fall semester. Starting with that student every 50th student is chosen until 75 students are included in the sample. What type of sampling is used?

Systematic

Define a sampling error.

The natural variation that results from selecting a sample to represent a larger population

Amy wants to estimate the mean grade point average of students at her school. She collects data by recording the grade point average of every 25th student on the list of students after a randomly selected first student. Biased or Unbiased?

Unbiased

To estimate the male to female ratio of the residents of her city, Janice collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents. Biased or Unbiased?

Unbiased

To estimate the mean number of classes that students take at his university, Raymond collects data from a randomly selected proportionate number of students from each grade level. Biased or Unbiased?

Unbiased

Define: Outlier

a data point that is distant from all the other data points

What is random sampling without replacement?

a member of the population may be chosen only once

Define: experimental unit

a single object or individual to be measured

Edward has created an experiment to test whether or not height has any effect on red blood cell count. Which of the following gives the explanatory and response variables, respectively, in this situation? a. height and red blood cell count b. red blood cell count and height c. the number of people in the experiment and red blood cell count d. the number of people in the experiment and height

a. height and red blood cell count

To determine whether or not number of siblings influences grade point average, Charles has designed a survey. What is the explanatory variable? a. number of siblings b. grade point average c. the number of people surveyed d. none of the above

a. number of siblings

After asking 11 randomly selected students from her school whether or not they read the newspaper, Gloria reports that 55% of the students from her school read the newspaper based on her survey. Why is this statistic misleading? a. sample size is insufficient b. the sample is biased c. the statistic contains a calculation error d. the data contains an outlier

a. the sample size is insufficient

Define Qualitative Data

aka categorical date - the result of categorizing or describing attributes of a population Ex: hair color, blood type, ethnic group, the car a person drives, the street a person lives on generally described by words or letters

What is quantitative discrete data?

all data that are the result of counting - take on only certain numerical values - Ex: one, two, three

Tina has created an experiment to test whether or not age has any effect on the number of words on a list that can be remembered. What is the explanatory variable in this situation? a. the number of people in the experiment b. age c. the number of words on a. list that can be remembered d. none of the above

b. age

Jason is collecting data on the number of books students read each year. What type of data is this? a. qualitative b. discrete quantitative c. continuous quantitative d. none of the above

b. discrete quantitative

Timothy is collecting data on the number of dental cavities. What type of data is this? a. qualitative b. discrete quantitative c. continuous quantitative d. none of the above

b. discrete quantitative

A political researcher asks people if they Strongly Disagree, Disagree, Agree, or Strongly Agree with various policy decisions. What is the level of measurement of the data? a. nominal b. ordinal c. interval d. ratio

b. ordinal

Clarence collected data from a random sample of 900 working residents in his town asking whether or not they commute less than 10 miles to work. Based on the results, he reports that 54% of the working residents in his state commute less than 10 miles to work. Why is this misleading? a. the data contains an outlier b. the sample is biased c. the statistic contains a calculation error d. the sample size is insufficient

b. the sample is biased

Howard collected data from a random sample of 600 people in his town asking whether or not they attend church. Based on the results, he reports that 48% of the people in his state attend church. Why is this statistic misleading? a. the data contains an outlier b. the sample is biased c. the sample size is insufficient d. the statistic contains a calculation error

b. the sample is biased

Rebecca collected data from a random sample of 500 homeowners in her state asking whether or not they use electric heat. Based on the results, she reports that 51% of the homeowners in the nation use electric heat. Why is this statistic misleading? a. The sample size is insufficient b. The statistic contains a calculation error c. The sample is biased d. The data contains an outlier.

c. The sample is biased

Given that Angelina is collecting data on commute distance, what type of data is she working with? a. qualitative b. discrete quantitative c. continuous quantitative d. none of the above

c. continuous quantitative

Given that Justin is collecting data on reaction time, what type of data is he working with? a. qualitative b. discrete quantitative c. continuous quantitative d. none of the above

c. continuous quantitative

Thomas is investigating if gender has any effect on political party associations. Which of the following gives the explanatory and response variables respectively? a. the number of people that are being studied and political party associations b. the number of people that are being studied and gender c. gender and political party associations d. political party associations and gender

c. gender and political party associations - explanatory is the independent variable, which is the variable that is changed to determine its effect on a dependent or response variable. - response variable is the variable being measured or tested in response to changes in the independent variable

A chef keeps track of the temperature of his refrigerator in degrees Celsius. What is the level of measurement of the data? a. nominal b. ordinal c. interval d. ratio

c. interval

A climate scientist keeps track of the daily temperature, in degrees Fahrenheit, of a lake over the course of six weeks. What is the level of measurement of the data? a. nominal b. ordinal c. interval d. ration

c. interval

After asking 8 randomly selected individuals from her city whether or not they were born within the state, Kathryn reports that 63% of the individuals from her city were born within the state based on her survey. Why is the statistic misleading? a. the sample is biased b. the data contains an outlier c. the sample size is insufficient d. the statistic contains a calculation error

c. the sample size is insufficient

What is in a pie chart?

categories of date represented by wedges in a circle and are proportional in size to the percent of individuals in each category

What is a pareto chart?

consists of bars that are sorted into order by category size (largest to smallest)

A biologist samples and measures the length of the fish in a lake. What is the level of measurement of the date? a. nominal b. ordinal c. interval d. ratio

d. ratio

A track runner keeps track of how long it takes her to run the 200 meter dash. What is the level of measurement of the data? a. nominal b. ordinal c. interval d. ratio

d. ratio

A cable provider advertises that their average package price is $74. given that their package prices are $14, $82, $94, and $106, why is this statistic misleading? a. the sample is biased b. the sample size is insufficient c. the statistic contains a calculation error d. the data contains an outlier

d. the data contains an outlier

What is quantitative continuous data?

data that are not only made up of counting numbers, but that may include fractions, decimals, or irrational numbers - often the result of measurements like length, weights, or times - Ex: 2.4, 7.5, or 11.0

How do you choose a stratified sample?

divide the population into groups called strata and then take a proportionate number from each stratum

Define: Bias

error present when date is collected from samples which are not representative of the entire population under study

What is random sampling with replacement?

once a member is picked, that member goes back into the population and thus may be chosen more than once

What are the two graphs used to display qualitative data?

pie charts and bar graphs

Quantitative (discrete or continuous) or Qualitative? the type of calculator you use

qualitative

Quantitative (discrete or continuous) or Qualitative? the type of car you drive

qualitative

Quantitative (discrete or continuous) or Qualitative? the distance it is from your home to the nearest grocery store

quantitative continuous

Quantitative (discrete or continuous) or Qualitative? weights of sumo wrestlers

quantitative continuous

Quantitative (discrete or continuous) or Qualitative? IQ scores

quantitative continuous (may cause some discussion)

The data are the weights of backpacks with books in them. You sample five students. The weights (in pounds) of the backpacks are 6.2, 7, 6.8, 0.1, 4.3. Notice that backpacks carrying three books can have different weights. What kind of data is this?

quantitative continuous data (weights)

Quantitative (discrete or continuous) or Qualitative? number of correct answers on a quiz

quantitative discrete

Quantitative (discrete or continuous) or Qualitative? the number of classes you take per school year

quantitative discrete

Quantitative (discrete or continuous) or Qualitative? the number of pairs of shoes you own

quantitative discrete

The data are the number of books students carry in their backpacks. You sample five students. Two students carry three books, one student carries four books, one student carries two books, and one student carries one book. What kind of data is this?

quantitative discrete data (the number of books: 3,4,2,1)

Define: cumulative relative frequency

the accumulation of the previous relative frequencies - add all the previous relative frequencies to the relative frequency for the current row - last entry should be 1 indicating that one hundred percent of the data has been accumulated

Define: treatments

the different values of the explanatory variable

What is in a bar graph?

the length of the bar for each category is proporitonal to the number or percent of individuals in each category. Bars may be vertical or horizontal.

Define: frequency

the number of times a value of the data occurs

A sample should have the same characteristics as what?

the population it is representing

Define: relative frequency

the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. - divide each frequency by the total number - can be written in fractions, percents, or decimals

Define Quantitative Data

the result of counting and measuring attributes of a population Ex: amount of money, pulse rate, weight, number of people living in your town, number of students who take statistics always numbers

You go to the supermarket and purchase three cans of soup (19 ounces tomato bisque, 14.1 ounces lentil, and 19 ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies) Name a data set that is quantitative discrete.

the three cans of soup, two packages of nuts, four kinds of vegetables and two desserts you can count them

You go to the supermarket and purchase three cans of soup (19 ounces tomato bisque, 14.1 ounces lentil, and 19 ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies) Name a data set that is quantitative continuous.

the weights of the soups (19 ounces, 14.1 ounces, 19 ounces) or the weights of the desserts (16 ounces, 32 ounces) you measure weights as precisely as possible

You go to the supermarket and purchase three cans of soup (19 ounces tomato bisque, 14.1 ounces lentil, and 19 ounces Italian wedding), two packages of nuts (walnuts and peanuts), four different kinds of vegetable (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies) Name a data set that is qualitative.

types of soups, nuts, vegetables and desserts categorial

Define: response variable

when one variable causes change in another - the affected variable is the response variable

Define: explanatory variable

when one variable causes change in another - the first variable is the explanatory variable

When can a pie chart not be used?

when percentages add to more or less than 100%