Trees:
A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal Model applies in this case.
1. Draw the Normal Model that represents the tree diameters found in the forest.
2. What size would you expect the central 95% of all trees to be? Explain.
3. About what percent of trees should be less than an inch in diameter? Explain.
4. About what percent of trees should be between 5.7 and 10.4 inches in diameter? Explain.
5. About what perent of the trees should be over 15 inches in diameter? Explain.
The Dutch Men: Let's think about the Normal Model for the heights of Dutch Men. Their mean height is 184cm and the standard deviation is 8cm. For each question below, sketch the Normal model, shade the diagram, and find the related z-score before determining the percentage. (Remember - many of these answers are not exact, so I will be looking for the reasoning and logic that led to your answer, not just a circled # on your page.) 1. What fraction of Dutch men should be less than 190cm tall? 2. What fraction of Dutch men should be between 170 and 180cm tall? 3. What fraction of Dutch men should be over 198cm tall? 4. How tall are the tallest 10% of all Dutch men? 5. How tall are the shortest 20% of Dutch men? 6. How tall are the middle 50% of Dutch men?
Football:
NFL data from the 2006 football season reported the number of yards gained by each of the 167 wide receivers in the league.
The mean of the data is 435 yards, with a standard deviation of 384 yards.
This graph shows those results:
1. Draw a Normal Model, shading the area under the curve that is less than 2 standard deviations below the mean.
2. According to the Normal Model, what percent of receivers would you expect to gain fewer yards than 2 standard deviations below the mean number of yards?
3. How many of the 167 wide receivers in the NFL would that percentage be talking about?
4. How does that compare to the actual data show in the graph above?
5. Explain the problem in using a Normal Model here. Why does it not work?
Normal Model Quiz:
Title this in your notebook Quiz: Properties of the Normal Curve.
Note: The multiple choice responses are percents written in decimal form.
For each problem, you should draw the model and shade (like we practiced in class before the break) - only need to mark the z-scores below for most.
You should be able to draw only one diagram to answer questions 6 - 11. (The directions for these questions are right below the title of the quiz on the page.)
Record your score upon completion and explain how to correctly come up with the right answer (for all those you got wrong).
Review:
There is a Review Sheet for this chapter on the Normal Model that Ms. Valente has in study for you to pick up at this time. (Period 3 already has received it.)
As you can assume, this will lead a collection of the notebooks upon my return.
When is that? might you ask... Friday, 27th.
Be sure that everything is written neatly, descriptively, and with titles so I can find things.
Take Notes in your notebook on all the lessons as well as answering the questions I've put in between...
many things are "said" and not written, so I will be looking for notes added in your own words, not only copying the screen in the video.
In the video, he mentions "inferential statistics"... what does that mean?
Make up your own definition after looking up the word "infer" (since that's the base of inferential).
In the example he's giving at the bottom... what is the population being discussed? Why was choosing the row of girls not ok?
What is "mutually exclusive"?
What is "homogeneous"?
Explain, in your own words, the difference between Simple Random Sampling and Stratified Random Sampling.
Use the example of a group of animals seen out on a safari. In this wildlife park, there are 100 elephants, 250 zebras, 13 ostrich, and 25 lions.
What is a census?
Flight Info:
We need to survey a random sample of the 300 passengers on a flight form San Francisco to Tokyo.
Name each sampling method described below AND state how you know it is this type of sampling.
1. Pick every 10th passenger as people board the plane.
2. From the boarding list, randomly choose 5 people flying first class and 25 of the other passengers.
3. Randomly generate 30 seat numbers and survey the passengers who sit there.
4. Randomly select a seat position (right window, right center, right aisle, etc.) and survey all the passengers sitting in those seats.
Making Claims:
Why is each of the following claims not correct?
1. It is always better to take a census than to draw a sample.
2. Stopping students on their way out of the cafeteria is a good way to sample if we want to know about the quality of the food there.
3. A poll taken on a statistics support website garnered 12.357 responses. The majority said they enjoy doing statistics homework. With a sample size that large, we can be pretty sure that most statistics students feel this way too.
Chicken Noodle Soup:
Chicken noodle soup can demonstrate what it means to be a good "representative sample". From your first spoonful of soup, you make a judgement on whether you like the soup or not.
1. Describe a spoonful of soup that you might take that would NOT be a good representation of the soup (and therefore NOT a "representative sample").
2. Describe the spoonful that you would take that WOULD BE a good "representative sample".
Cafeteria:
The Food Service staff need to find out some information on how students feel about the importance of the salad bar at school.
Is it important that students have eaten at the salad bar to participate in this survey?
Thinking of a high school cafeteria in the movies, where everyone eats at the same time (like in Mean Girls or The High school Musical), describe how would you conduct a survey using each of the following types of sampling.
1. Simple Random Sampling
2. Stratified Random Sampling
3. Cluster Sampling
4. Systematic Random Sampling
5. The Food Service staff believe that men and women typically have different opinions about the importance of the salad bar. Which sampling strategy would be best to allow for this difference between men and women?
School Uniforms:
1. What is wrong with the way the student initially chose to do his survey?
Give at least three reasons why this was not a successful collection of data to help him argue his point to the School Governing Board.
2. Why did they need to use a stratified sampling in this situation?
3. When choosing the individual people to participate in the survey, he gave two methods (first was drawing numbers form a bag).
What type of sampling would the second method be considered? Explain.
Freshmen and Food:
You are trying to find out what freshmen think of the food served on campus and have thought of a couple of sampling methods...
How do you feel about these options? Explain what is wrong with these ideas and what kind of sampling is being used.
1. First set up a "Tell Us What You Think" website and invite freshmen to visit the site to complete a questionnaire there.
2. Just stand outside the school cafeteria at lunchtime and stop people to ask them the questions on your survey.
Only need to watch the first 2 min and 20 seconds!!
Pick up: 11.4 Random Samples and Surveys Worksheet from Ms. Valente.
Dots, Dots, and more Dots:
Once you're on this site, if you can, enlarge the screen so you have a good view of the circle activity.
Click "Start" Interactive Activity and follow the directions on the first tab. Interactive Activity
What do you notice about your result (the average diameter of the circles) vs. the results you see from the other two tabs?
Why do you think this is the case?
What is this an example of?
What type of sampling did you use here?
Ms. Valente has a Paper Quiz for you to take on Sampling and Bias.
You can pick up the quiz on Wednesday and it MUST be turned in to Ms. Valente on Thursday!!
DON'T FORGET TO DO THIS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
DON'T FORGET - I WILL BE COLLECTING YOUR NOTEBOOKS ON FRIDAY IN CLASS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
If you did not receive this paper last week, or forgot it at school, or did not complete it... make sure you do it:
The Normal Model Experiment:
Period 1 and Period 4
Period 3
Period 7
Trees:
A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal Model applies in this case.
1. Draw the Normal Model that represents the tree diameters found in the forest.
2. What size would you expect the central 95% of all trees to be? Explain.
3. About what percent of trees should be less than an inch in diameter? Explain.
4. About what percent of trees should be between 5.7 and 10.4 inches in diameter? Explain.
5. About what perent of the trees should be over 15 inches in diameter? Explain.
The Dutch Men:
Let's think about the Normal Model for the heights of Dutch Men. Their mean height is 184cm and the standard deviation is 8cm. For each question below, sketch the Normal model, shade the diagram, and find the related z-score before determining the percentage. (Remember - many of these answers are not exact, so I will be looking for the reasoning and logic that led to your answer, not just a circled # on your page.)
1. What fraction of Dutch men should be less than 190cm tall?
2. What fraction of Dutch men should be between 170 and 180cm tall?
3. What fraction of Dutch men should be over 198cm tall?
4. How tall are the tallest 10% of all Dutch men?
5. How tall are the shortest 20% of Dutch men?
6. How tall are the middle 50% of Dutch men?
Football:
NFL data from the 2006 football season reported the number of yards gained by each of the 167 wide receivers in the league.
The mean of the data is 435 yards, with a standard deviation of 384 yards.
This graph shows those results:
1. Draw a Normal Model, shading the area under the curve that is less than 2 standard deviations below the mean.
2. According to the Normal Model, what percent of receivers would you expect to gain fewer yards than 2 standard deviations below the mean number of yards?
3. How many of the 167 wide receivers in the NFL would that percentage be talking about?
4. How does that compare to the actual data show in the graph above?
5. Explain the problem in using a Normal Model here. Why does it not work?
Normal Model Quiz:
Title this in your notebook Quiz: Properties of the Normal Curve.
Note: The multiple choice responses are percents written in decimal form.
For each problem, you should draw the model and shade (like we practiced in class before the break) - only need to mark the z-scores below for most.
You should be able to draw only one diagram to answer questions 6 - 11. (The directions for these questions are right below the title of the quiz on the page.)
Record your score upon completion and explain how to correctly come up with the right answer (for all those you got wrong).
Review:
There is a Review Sheet for this chapter on the Normal Model that Ms. Valente has in study for you to pick up at this time. (Period 3 already has received it.)
As you can assume, this will lead a collection of the notebooks upon my return.
When is that? might you ask... Friday, 27th.
Be sure that everything is written neatly, descriptively, and with titles so I can find things.
Take Notes in your notebook on all the lessons as well as answering the questions I've put in between...
many things are "said" and not written, so I will be looking for notes added in your own words, not only copying the screen in the video.
In the video, he mentions "inferential statistics"... what does that mean?
Make up your own definition after looking up the word "infer" (since that's the base of inferential).
Briefly explain:
What is the difference between difference between Descriptive and Inferential Statistics?
In the example he's giving at the bottom... what is the population being discussed? Why was choosing the row of girls not ok?
What is "mutually exclusive"?
What is "homogeneous"?
Explain, in your own words, the difference between Simple Random Sampling and Stratified Random Sampling.
Use the example of a group of animals seen out on a safari. In this wildlife park, there are 100 elephants, 250 zebras, 13 ostrich, and 25 lions.
What is a census?
Flight Info:
We need to survey a random sample of the 300 passengers on a flight form San Francisco to Tokyo.
Name each sampling method described below AND state how you know it is this type of sampling.
1. Pick every 10th passenger as people board the plane.
2. From the boarding list, randomly choose 5 people flying first class and 25 of the other passengers.
3. Randomly generate 30 seat numbers and survey the passengers who sit there.
4. Randomly select a seat position (right window, right center, right aisle, etc.) and survey all the passengers sitting in those seats.
Making Claims:
Why is each of the following claims not correct?
1. It is always better to take a census than to draw a sample.
2. Stopping students on their way out of the cafeteria is a good way to sample if we want to know about the quality of the food there.
3. A poll taken on a statistics support website garnered 12.357 responses. The majority said they enjoy doing statistics homework. With a sample size that large, we can be pretty sure that most statistics students feel this way too.
Chicken Noodle Soup:
Chicken noodle soup can demonstrate what it means to be a good "representative sample". From your first spoonful of soup, you make a judgement on whether you like the soup or not.
1. Describe a spoonful of soup that you might take that would NOT be a good representation of the soup (and therefore NOT a "representative sample").
2. Describe the spoonful that you would take that WOULD BE a good "representative sample".
Cafeteria:
The Food Service staff need to find out some information on how students feel about the importance of the salad bar at school.
Is it important that students have eaten at the salad bar to participate in this survey?
Thinking of a high school cafeteria in the movies, where everyone eats at the same time (like in Mean Girls or The High school Musical), describe how would you conduct a survey using each of the following types of sampling.
1. Simple Random Sampling
2. Stratified Random Sampling
3. Cluster Sampling
4. Systematic Random Sampling
5. The Food Service staff believe that men and women typically have different opinions about the importance of the salad bar. Which sampling strategy would be best to allow for this difference between men and women?
School Uniforms:
1. What is wrong with the way the student initially chose to do his survey?
Give at least three reasons why this was not a successful collection of data to help him argue his point to the School Governing Board.
2. Why did they need to use a stratified sampling in this situation?
3. When choosing the individual people to participate in the survey, he gave two methods (first was drawing numbers form a bag).
What type of sampling would the second method be considered? Explain.
Freshmen and Food:
You are trying to find out what freshmen think of the food served on campus and have thought of a couple of sampling methods...
How do you feel about these options? Explain what is wrong with these ideas and what kind of sampling is being used.
1. First set up a "Tell Us What You Think" website and invite freshmen to visit the site to complete a questionnaire there.
2. Just stand outside the school cafeteria at lunchtime and stop people to ask them the questions on your survey.
Only need to watch the first 2 min and 20 seconds!!
Pick up: 11.4 Random Samples and Surveys Worksheet from Ms. Valente.
Dots, Dots, and more Dots:
Once you're on this site, if you can, enlarge the screen so you have a good view of the circle activity.
Click "Start" Interactive Activity and follow the directions on the first tab.
Interactive Activity
What do you notice about your result (the average diameter of the circles) vs. the results you see from the other two tabs?
Why do you think this is the case?
What is this an example of?
What type of sampling did you use here?
Take the quiz on the following site: Multiple Choice Quiz on Sampling Randomly and Non-Randomly
Record your score after you submit your answers AND record the numbers of all the questions you answered incorrectly!!
Ms. Valente has a Paper Quiz for you to take on Sampling and Bias.
You can pick up the quiz on Wednesday and it MUST be turned in to Ms. Valente on Thursday!!
DON'T FORGET TO DO THIS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
DON'T FORGET - I WILL BE COLLECTING YOUR NOTEBOOKS ON FRIDAY IN CLASS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!