Vocabulary
This allows individuals from each group within a population to be represented in the sample set.
Random Sampling
The teachers in a school are asked to send four students from their homerooms to represent the class. Mr. Burts puts the names of all the students in a box, mixes the names, and pulls out four names without looking. Is this biased or unbiased?
. Is this biased or unbiased?
Unbiased
Mr. Burr’s method creates a random sample.
Clayton completes a report by asking 70 students across campus. She found that 48% of CTMS students do not wash their hands after using the bathroom. What is the sample size?
a. 70
b. 48
c. all CTMS students
a. 70
A survey company is trying to determine if people in a certain state think that pollution is too high.
Which choice BEST represents the population?
a. Every person who owns more than 2 cars.
b. All the people who live in wealthy neighborhoods.
c. All the people who live in dirty neighborhoods.
d. Every person that lives in the state.
d. Every person that lives in the state.
A business magazine surveys 500 of its subscribers and determines that the median of their annual salaries is $48,000. Which choice is a valid inference in this situation?
A) All of the subscribers make at least $48,000.
B) 50% of the subscribers make more than $48,000.
C) None of the subscribers earn more than $48,000.
D) At least 60% of the subscribers make less than $48,000.
B. 50% of the subscribers make more than $48,000.
The median value is the "middle" value. 50% of the population makes more than the median, and 50% of the population makes less than the median.
This is an entire group considered for a survey
Population
Eight citizens are asked their opinions about what trash should be collected. Is this biased or unbiased?
Biased, sample size too small
Each student's name is written on a piece of paper. The names are placed in a bowl, and names are picked without looking.
Random Sampling
A mayor wants to determine if the people in his city think that he is doing a good job.
Which choice BEST represents the population?
a. All the local business owners.
b. Voters age 21 to 35.
c. The people who voted for him.
d. All the residents of the city.
d. All the residents of the city.
The Nashville Humane Society records the weights of 250 cats that are taken in during the month of July. The mean weight of the cats is 7.5 pounds. Which statement is a valid inference in this situation?
a. All 250 cats weighed exactly 7.5 pounds.
b. All 250 cats weighed close to 7.5 pounds.
c. None of the cats weighed more than 7.5 pounds.
d. At least 50% of the 250 cats weighed at least 7.5 pounds.
b. All 250 cats weighed close to 7.5 pounds.
The mean is the average weight of all the cats brought into the Nashville Humane Society during the month of July.
This is a sample that does not represent the whole population
Biased
Each math class randomly selects two students do represent their class on an advisory panel being assembled by the principal
Unbiased, random
A musician wants to determine what the people who bought his last album thought about the songs.
Which choice BEST represents a sample?
a. Every person who bought the album.
b. A selection of 250 people who bought the album.
c. A selection of 250 people who didn't buy the album
b. A selection of 250 people who bought the album.
Remember that a population data set contains all members of a specified group. A sample data set contains a part, or a subset, of a population.
Data set 1: 1, 2, 3, 4, 5
Date set 2: 2, 4, 6, 8, 10
What is the difference between the medians?
3
A recent survey of 800 seventh graders from across the state shows 4 out of 10 like to play paper football. How many students said they like to play paper football?
320 students
.4 x 800
This variable is subject to random variation if its value is not predictable.
Random Variable
A survey is conducted at the local shopping mall about household products used on a daily basis.
Biased, only customers at the shopping mall have an opportunity to be surveyed
At the end of the city's annual marathon, each participant completed a questionnaire. The marathon's planner chose 30 of the surveys to review. Which statement BEST describes the random sample?
A) The 30 surveys are likely to be representative of all the runners in the marathon.
B)The 30 surveys are likely to be representative of all who came to watch the marathon.
C)The 30 surveys are not likely to be representative of all the runners in the marathon.
D)The 30 surveys are likely to be representative of only the runners placed in the marathon.
The 30 surveys are likely to be representative of all the runners in the marathon.
All runners in the marathon filled out a survey; therefore, the sample represents that population.
A teacher wants to select five students from the class. Suppose that the classroom has six rows of chairs with five chairs in each row. The teacher assigns the rows the digits 1 through 6. She throws a die and selects all the students in the row corresponding to the number on the die in the sample.
No (each student does not have an equally likely chance to be chosen and the students picked on dependent on each other)
A local pizza restaurant surveyed a random sample of 150 people that live in their town about their favorite type of pizza. Of the people surveyed, 40 said that pepperoni pizza was their favorite type of pizza. There are 2,800 residents that live in the town.
Based on the data, is 750 a reasonable estimate for the number of residents in the town whose favorite pizza is pepperoni?
a. No, because the proportion of the sample whose favorite pizza is pepperoni is about 27%.
b. Yes, because the proportion of the sample whose favorite pizza is pepperoni is about 27%.
c. No, because the proportion of the sample whose favorite pizza is pepperoni is about 40%.
d. Yes, because the proportion of the sample whose favorite pizza is pepperoni is about 40%.
Yes, because the proportion of the sample whose favorite pizza is pepperoni is about 27%.
pepperoni = 40/150 = .27 x 2,800 = 756
This is a subset of a population that seeks to accurately reflect the characteristics of the larger group.
Representative Sample
A shirt manufacturer wants to check quality control of their products. The plant manager decides to check every 5th shirt inspected by Inspector D. There are 15 inspectors in the plant.
Biased, only Inspector D’s shirts are being checked
A librarian is interested in the numbers of books that visitors check out from the library. She examines the checkout records of 250 randomly selected adult visitors.
Identify the population and sample for this situation.
A. The population is all visitors of the library; the sample is the adult visitors of the library
B. The population is all adult visitors of the library; the sample is the 250 visitors selected.
C. The population is all visitors who check out at least 1 book from the library; the sample is the 250 visitors selected.
D. The population is the 250 visitors selected; the sample is the 250 visitors who check out at least 1 book from the library.
B. The population is all adult visitors of the library; the sample is the 250 visitors selected.
Remember, the population is the entire group of people or things to be studied. The sample is part of the population.
You have a jar filled with skittles and 10 skittles were on the table. Which one is the population: the jar filled with skittles or the skittles on the table?
The jar filled with skittles
A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which inferences can appropriately be drawn from this survey result?
a. At least 95% of people who go see movies will dislike this movie.
b. At least 95% of people who read books will dislike this movie.
c. Most people who dislike the book will like this movie.
d. Most people who like the book will dislike this movie.
d. Most people who like the book will dislike this movie.
Statistical inference is the process of drawing conclusions about an underlying population based on a sample.