Secondary Math 3

Unit 4.1 – Statistical Inferences

Objectives

-Students will understand that statistics allows inferences to be made about population parameters based on a random sample from that population.

-Students will can distinguish between different sampling methods and choose an appropriate method for a given situation.

Notes:

Notes continued:

Assignment 4.1

Define the following vocabulary in your own words

  1. Population:
  1. Sample:
  1. Parameter of Interest:
  1. Population Parameter:
  1. Simple Random Sample:
  1. Systematic Sample:
  1. Stratified Sample:
  1. Cluster Sample:
  1. Convenience Sample:
  1. Volunteer Sample:

Identify if the following are examples of parameters of interest or populations.

  1. All four-inch ham sandwiches sold at Quizno’s.
  2. The average weight in ounces of all four-inch ham sandwiches sold at Quizno’s.
  3. The proportion of registered drivers in California who had an accident in 2008.
  4. All apartment units in New York that are larger than 2000 square feet.
  5. The percentage of dogs and cats in Los Angeles that have been spayed or neutered.
  6. All 100 members of the United States Senate.

For each situation described, identify a) the population, b) the sample, and c) the parameter of interest.

  1. An AP Government class wants to know the percentage of eligible voters in the state of Utah who voted in the most recent election. There are 1,938,249 people in Utah who are 18 and older. The class randomly looks at 15 state house districts and discovers that 50.5% of the eligible voters actually voted.
  2. A local radio station has added an additional radio personality and is trying to determine what type of music to play during this person’s air time. This time slot is geared towards teenage listeners. The station has decided to survey 300 randomly selected students from the ages of 13 to 19.
  1. A health class wants to know the average amount of time Utahns over the age of 12 spend exercising each week. A sample of 1,200 randomly selected people, over the age of 12, across the state was surveyed.
  1. CBS News conducted a public opinion survey between February 5th and 10th, 2010. 1,084 randomly selected adults from across the United States were contacted and asked the question, “Do you approve or disapprove of the way Barack Obama is handling his job as president?”

For each method described below, determine what type of sampling method it is and justify whether or not the method is biased.

  1. In order to determine the average composite score on the most recent ACT exam, students were divided into groups based on whether they were enrolled in remedial, regular, or honors language arts. Individual scores were randomly selected from each group.
  1. Every third patron exiting the school musical was surveyed regarding their support for more funding of the arts.
  1. A random number generator was used to assign students to demonstrate work in front of the class.
  1. A news show asks viewers to participate in an on-line poll.
  1. A civil engineering student, working on his thesis, plans a survey to determine the proportion of all current drivers that regularly wear a seat belt. He decides to interviewhis classmates in the three classes he is currently enrolled in.
  1. In the parking lot cars are separated by color and all red cars and all yellow cars have their tire pressure tested.

4.2 – Sampling, Observational Studies, and Experiments

Objectives

-Students will recognize the purposes of and differences among sample surveys, experiments, and observational studies and how randomization relates to each.

-Students will evaluate reports based on data.

Notes:

Notes continued:

Answer each of the following questions, circle your answer. Separate the questions and identify if you are male or female on each one.

Secondary Math 3

  1. What is your favorite style of music?
  2. Rock
  3. Hip-hop
  4. Rap
  5. Punk
  6. Other
  1. What is your favorite type of food?
  2. Chinese
  3. Mexican
  4. Italian
  5. American
  6. Other
  1. What is your favorite flavor of ice cream?
  2. Chocolate
  3. Vanilla
  4. Strawberry
  5. Cookie and Cream
  6. Other
  1. What is your favorite color?
  2. Blue
  3. Green
  4. Red
  5. Purple
  6. Other
  1. What is your favorite type of movie?
  2. Drama
  3. Comedy
  4. Mystery
  5. Horror
  6. Other

  1. What is your favorite type of sandwich?
  2. Hamburger/Cheeseburger
  3. Chicken
  4. Ham
  5. Turkey
  6. Other
  1. What is your favorite gaming system?
  2. X-box
  3. PS3
  4. Wii
  5. Nintendo 64
  6. Other
  1. What is your favorite soda?
  2. Coca-Cola
  3. Pepsi
  4. Dr. Pepper
  5. Mountain Dew
  6. Other
  1. What is your favorite store?
  2. Hollister
  3. Aeropostale
  4. American Eagle
  5. Abercrombie and Fitch
  6. Other
  1. What is your favorite past time?
  2. Reading
  3. Listening to music
  4. Watching TV
  5. Sports
  6. Other

Secondary Math 3

Sampling and Surveys

Period______Question #______Number of Responses ______Males______Females______

  1. Create a frequency table displaying the results of your question from the survey.

Answer / A / B / C / D / E
Frequency
  1. Calculate the probabilities for each of the following responses to your question.

Answer / A / B / C / D / E
Probability
  1. Assume there are 2000 students at Fremont High School. Use the data from the entire class to estimate the number of students who would respond to your question with each response.

Answer / A / B / C / D / E
# of students

Simple Random Sample

Conduct a simple random sample of 12 responses from the responses to your question.

  1. Calculate the probabilities for each of the following responses from your random sample

Answer / A / B / C / D / E
Probability

Systematic Sample

Conduct a systematic sample of 12 responses from the responses to your question.

  1. Describe how you set up your systematic sample.
  1. Calculate the probabilities for each of the following responses from your systematic sample.

Answer / A / B / C / D / E
Probability

Stratified Sample

Conduct a stratified sample of 12 responses from the responses to your question.

  1. Describe how you set up your stratified sample.
  1. Calculate the probabilities for each of the following responses from your stratified sample.

Answer / A / B / C / D / E
Probability
  1. Are the sample probabilities similar to the population probabilities? If not, explain why they may be different.

Assignment 4.2:

  1. You want to ask a sample of high school students the question “how much do you trust information about health that you find on the Internet – a great deal, somewhat, not much, or not at all?” You try out this and other questions on a pilot group of 5 students chosen from your class. The class members are listed below. Use the following line of random digits to select a sample of five students: 19223 95034 05756 28713 96409 12531 42544 82853

Secondary Math 3

Anderson

Arroyo

Batista

Bell

Burke

Cabrera

Delluci

Deng

Eckstein

Fernandez

Fullmer

Gandhi

Glause

Helling

Johnons

Kim

Molina

Morgan

Murphy

Nguyen

Palmiero

Richards

Rider

Samuels

Tse

Velasco

Wallace

Zabidi

Secondary Math 3

  1. You are planning a report on apartment living in a college town. You decide to select three apartment complexes at random for in=depth interviews with residents. Obtain two different simple random sample of 5 from the listed apartments using the following lines of random digits. First Sample: 71870 99842 90771 48696 16834 70526 2224

Second Sample: 0751188915412671685384569793673433703316

Secondary Math 3

Ashley Oaks

Beau Jardin

Bluffs

Brandon Place

Brarwood

Brownstone

Burberry

Cambridge

Courts

Courthouse

Crestview

Del-Lynn

Farington

Fairway Knolls

Georgetown

Greenacres

Lahr House

Mayfair

Nay Pointe

Pemberly

Richfield

Ridge

Salem

Sagamore

Village

Waterford

Williamsburg

Secondary Math 3

Secondary Math 3

  1. Your statistics class has 30 students. You want to call a simple random sample of 5 students from your class to ask where they use a computer for the online exercises. You label the students 01, 02,…, 30. You enter the table of random digits at this line:

1445926056314248037165103622532249061181

Your simple random sample will contain what labeled students?

  1. A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to survey 120 guests who stayed at the hotel during a convention about their overall satisfaction with the property.

a. Explain why choosing a stratified random sample might be preferable to a simple random sample in this case. What would you use as strata?

b. Why might a cluster sample be a simpler option? What would you use as clusters?

Determine if the following are an experiment or an observational study.

Secondary Math 3

  1. The owner of a bakery collects data about the types of cupcakes that are purchased so she can make cupcakes accordingly. She records the type of cupcake purchased by every other person each day for three weeks.
  1. A botanist tests a new breed of plant by planting seeds from the new breed of plant and the traditional breed of plant in the same soil and the same location. He ensures that both types received the same amount of water and plant food. He records the growth rates of each plant.

Secondary Math 3

Secondary Math 3

  1. Every day for two weeks, a student records the number of her classmates who are late to class.
  1. A local grocery store selects 350 customers from a list of 1500 new customers in the past year to mail a questionnaire. There are 245 customers who return the questionnaire.

Secondary Math 3

  1. A teacher wants to know if playing classical music while a class works on a test will improve their scores on the test. She uses two class periods of equal size and equal baseline test data. For an entire semester, she plays classical music while one class is testing and plays no music while the other class is testing.
  1. A University of Helsinki (Finland) study wanted to determine if chocolate consumption during pregnancy had an effect on infant temperament at age 6 months. Researchers began by asking 305 healthy pregnant women to report their chocolate consumption. Six months after birth, the researchers asked mothers to rate their infants’ temperament, including smiling, laughter, and fear. The babies born to women who had been eating chocolate daily during pregnancy were found to be more active and “positively reactive” – a measure that the investigator said encompasses traits like smiling and laughter.
  2. Was this an observational study or an experiment? How do you know?
  1. What are the explanatory and response variables?
  1. Does this study show that eating chocolate regularly during pregnancy helps produce infants with good temperament? Explain.
  1. An educator wants to compare the effectiveness of computer software for teaching biology with that of a textbook presentation. She gives a biology pretest to each of a group of high school juniors, then randomly divides them into two groups.
  2. Is this an observational study or an experiment? Justify your answer.
  1. If the group using the computer has a much higher average increase in test scores than the group using the text book, what conclusions, if any, could the educator draw?
  1. You can use Voice over Internet Protocol (VoIP) to make long-distance telephone calls over the Internet. How will the cost affect the use of this service? A university plans an experiment to find out. It will offer the service to all350 students in one of its dormitories. Some students will pay a low flat rate. Others will pay higher rates at peak periods and very low rates off-peak. The university is interested in the amount and time of use and in the effect on the congestion of the network. Identify the experimental units, the explanatory variables, the treatments, and the response variables.
  1. What is the most important advantage of experiments over observational studies?

Unit 4.3 – Simulations in Statistics

Objectives

-Students will understand the differences and similarities between theoretical and experimental probability.

-Students will be able to design a simulation to model a given situation.

Notes:

Notes Continued:

Assignment 4.3

Fill in the blank with the correct type of probability.

  1. The ______probability of an event occurring is the ratio of the number of favorable outcomes to the total number of outcomes.
  2. The probability that we calculate from data we collect is the ______probability.
  1. What does the “Law of Large Numbers” state?
  1. Clara got an A on 80% of her first semester quizzes. Design a simulation using each of the following methods to estimate the probability that she will get an A on a second semester quiz.

a)Random Number Generator:

b)Colored Marbles:

  1. Use the following simulated frequency table to determine the probability of Clara earning an A on her next quiz. Compare the experimental and theoretical probabilities from #4 and #5. If they are different, explain a possible reason why.

Outcome / Frequency / Probability
A / 17
Below an A / 3
Total / 20
  1. Three classes are offered at a gym; yoga, swimming, and kick-boxing. The ratio of members participating in each class is as follows: yoga – 1/3, swimming – 1/2, and kick-boxing – 1/6. Design a simulation using each of the following methods to estimate the probability of a new member taking each class.

1)Random Number Generator:

2)Rolling a die:

  1. Use the following simulated frequency table to determine the experimental probability of a member taking each of the offered classes. How could you make the experimental probabilities closer to the theoretical probabilities?

Outcome / Yoga / Swimming / Kick-boxing / Total
Frequency / 4 / 13 / 3 / 20
Probability
  1. Steve is a member of a bowling club. Last season he bowled a strike 60% of the time. Design a simulation using colored marbles to estimate the probability of Steve bowling a strike.
  1. Five students are being randomly selected from the school to receive a reserved parking pass. Assuming the school is 50% male and 50% female, design and run a simulation to determine the experimental probability of three or more females being selected to receive the parking pass. (Run 20 trials of the simulation)

Trial # / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
# of Females

Design:

Experimental probability of three or more females being selected:

  1. Four athletes will be randomly selected from the track team to represent the team at a school assembly. The team is 40% male and 60% female. Design and run a simulation to determine the experimental probability of only one male being selected for the assembly. (Run 20 trials of the simulation)

Trial # / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
# of Males

Design:

Experimental probability of only one male being selected:

  1. The local newspaper randomly selects 10 students for an interview about the school dress code. Nine of the students are boys. Does the number of boys selected cause you to question the selection process? Why or why not?

4.4Distributions

Objectives:

  • Define a population of interest and a sample that accurately reflects population.
  • Collect data answering a question about population.
  • Display data visually.
  • Calculate statistics.
  • Comment on the shape and skewedness, and whether the results were at all surprising.

Notes:

Notes continued:

Assignment 4.4

Data Distribution Project

Student: Your objective is to determine a population of interest and a question about that population. Then take a sample of the population. Graph your data collected. Calculate the statistics related to the data. Comment on the shape, skew, center, spread, and outliers of the data. Lastly, conclude by commenting on the results in relation to the population.

Some example topics:

Average height of students at school?

How many pairs of shoes does any given person have at the school?

How much sleep does any given student get per night on average?

Distance traveled to school?

Advanced / Basic / Below Basic
Population / • States a clear population of interest
(5-4 pts) / -Mostly states a clear population of interest
(3-2 pts) / • Does not state a population of interest
(1-0 pts)
Sample / -Clearly comments on whether sample is an accurate representation of the population
(5-4 pts) / Mostly comments on whether sample is an accurate representation of the population
(3-2 pts) / -Does not comment on whether sample is an accurate representation of the population
(1-0 pts)
Method of Collecting Data / -Well defined and randomization was used
(10-8 pts) / -Mostly defined and/or randomization was mostly used
(7-4 pts) / -Does not define and/or randomization was weakly used
(3-0 pts)
Graphical Representation of Data / -A histogram used to accurately displays:
1) a quantitative variable
2) with both axis's labeled
3) the x-axis labeled with numbers.
(10-8 pts) / -Missing one or two requirements from advanced.
(7-4 pts) / -Missing more than 3 requirements from advanced.
(3-0 pts)
Statistics of Data / -Accurately calculates and labels on the graph of the distribution:
1) mean
2) median
3) standard
deviation
and describes method for calculation (calculator, formula, ect.)
(10-8 pts) / -Mostly accurately calculates and/or labels on the graph of the distribution:
1) mean
2) median
3) standard deviation
and/or describes method for calculation (calculator, formula, ect.)
(7-4 pts) / -Does not accurately calculates and/or labels on the graph of the distribution:
1) mean
2) median
3) standard deviation
and/or describes method for calculation (calculator, formula, ect.)
(3-0 pts)
Interpret Data
and Conclusion
/ -Accurately comments on:
1) shape
2) skewness
3) center
4) spread
5) outliers
-Accurately makes a final comment on the results from the data in relation to population
(10-8 pts) / -Mostly accurately comments on at least 3 of the following topics:
1) shape
2) skewness
3) center
4) spread
5) outliers
-Mostly accurately makes a final comment on the results from the data in relation to population
(7-4 pts) / -Does not or does not accurately comments on:
1) shape
2) skewness
3) center
4) spread
5) outliers
-Does not or does not accurately make a final comment on the results from the data in relation to population
(3-0 pts)

Unit 4.5 – Normal Distribution

Objectives

-Students will use the mean and standard deviation of a data set to fit it to a normal distribution and estimate population percentages.