Name_______________________________________
Guided Notes Chapter 8
Chapter 8 – Section 1 – Random Samples and Surveys
Population: a ______________ of objects or people
Sample: a __________ of the population
Random Sample: when each member of the population has the ____________________ of being selected
Biased Question: a question that makes an unjustified _________________ or makes some answers
appear better than others.
Identifying a Random Sample
1) You survey customers at a mall. You want to know which stores they shop at most. Which sample is
more likely to be random?
a) You survey shoppers in a computer store.
b) You walk around the mall and survey shoppers.
2) You survey a store’s customers. You ask why they chose the store. Which sample is more likely to be
random?
a) You survey 20 people at the entrance from 5:00pm to 8:00pm.
b) You survey 20 people at the entrance throughout the day.
Identifying Biased Questions
3) Is each question biased or fair?
a)
“Do you think that soothing classical music is more pleasing than the loud, obnoxious pop
music that teenagers listen to?”
b) “Which do you think is the most common age group of people who like pop music?”
c) “Do you prefer classical music or pop music?”
4) Is each question biased or fair?
a) Do you prefer greasy meat or healthy vegetables on your pizza?
b) Which pizza topping do you like best?
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ChallengeA newspaper surveys 3 out of every 100 people of voting age in a community. The community has 38,592
people of voting age. How many people are surveyed?
ClosureIs the following question biased or fair? If it is biased, underline the word(s) that make you feel that way.
Do you prefer to play games on your computer or do boring homework?
Bell Ringer1) You want to survey people about their favorite exercise. Which sample below is more likely to be
random?
a) You ask people on a jogging track in a park to name their favorite exercise.
b) You ask people on their lunch hour at a downtown intersection to name their favorite exercise.
2) Is each question biased or fair?
a) Which is a brighter color, pink or green?
b) Is an electric pink shirt brighter than a green shirt?
Chapter 8 – Section 2 – Estimating Population Size
𝑛𝑢𝑚𝑏𝑒𝑟 𝑐𝑜𝑢𝑛𝑡𝑒𝑑 𝑡ℎ𝑎𝑡 𝑎𝑟𝑒 𝑚𝑎𝑟𝑘𝑒𝑑
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑐𝑜𝑢𝑛𝑡𝑒𝑑
=
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑚𝑎𝑟𝑘𝑒𝑑
𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
Using the Capture/Recapture Method1) Researchers count 48 marked deer and a total of 638 deer on a flight over an area. They know there are
105 marked deer. Write a proportion to estimate the deer population in the area.
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2) Suppose the researchers in Example 1 count 638 deer, but only 35 marked deer. Estimate the total deer
population in the area.
3) There are 30 marked seals. In a survey, you count 58 seals, 16 of which were marked. About how many
seals are in the area?
ChallengeIn a capture/recapture program, 30% of the animals recaptured have tags. Suppose 70 animals were
originally captured, tagged and released. Estimate the population.
Closure
Use a proportion to estimate the population of each.
1) Total bison counted: 350
Tagged bison counted: 45
Total tagged bison: 100
2) Total elk counted: 675
Marked elk counted: 123
Total marked elk: 465
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Bell RingerUse a proportion to estimate each animal population.
1) Total Trout Counted: 4,000
Tagged Trout Counted: 350
Total Tagged Trout: 2,500
2) Total Rabbits Counted: 685
Tagged Rabbits Counted: 235
Total Tagged Rabbits: 550
Chapter 8 – Section 3 – Inferences
Inference: a ________________ or conclusion based on data or reasoning
Drawing Inferences about a Population
1) A restaurant manager selected a random sample of 20 customers and recorded the amount they spend
on their meal. Based on the sample, which is the best estimate of the average, or mean, amount that
customers spend on a meal at the restaurant?
Step 1: Find the average, mean, of the data.
Step 2: Use the average to draw an inference.
2) Use the random sample from Example 1. Draw an inference about the percent of customers at the
restaurant who spend more than $20. Support your answer.
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Comparing Random Samples
3) There are 360 students at a middle school. Sonya, Jane, and Danny each survey a random sample of 25
students about whom they plan to vote for in the election for student council president. Their results are
shown below in the table.
a) For each sample, predict how many votes Carlos will get.
Use a proportion.
𝑣𝑜𝑡𝑒𝑠 𝑓𝑜𝑟 𝐶𝑎𝑟𝑙𝑜𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒
𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑣𝑜𝑡𝑒𝑠 𝑓𝑜𝑟 𝐶𝑎𝑟𝑙𝑜𝑠
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠 𝑖𝑛 𝑠𝑐ℎ𝑜𝑜𝑙
Sonya’s Sample:
Jane’s Sample:
Danny’s Sample:
b) Describe the variation in the prediction. Variation = Range
c) Draw an inference about the number of votes Carlos will get.
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4) The table shows the results of 3 random samples of 30 students each at a middle school with 420
students. The students were asked how many hours they spend online each week.
a) For each sample, predict how many students in the school spend at least 5 hours online per week.
Sample 1
Sample 2
Sample 3
b) Describe the variation in the prediction.
c) Draw an inference about the number of students in the school who spend at least 5 hours online per
week.
Challenge
A government inspector takes 5 random samples of the same size from a shipment of eggs. She
determines the mean weight of a dozen eggs in each sample. What can the inspector conclude if the mean
weights of the samples are very close to each other?
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Closure
1) There are 135 people enrolled in morning activities at the local recreation department. The director
surveys 3 random samples of 20 participants each about which activities they plan to attend in the
mornings. Her results are shown in the table.
a) For each sample, predict how many participate in yoga.
Sample 1
Sample 2
Sample 3
b) Describe the variation in the predictions.
c) Make an inference about the number of people enrolled in yoga.
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Bell Ringer1) There are 275 students in the senior class. The class president surveys 3 random samples of 25 students
each about their choice for class song.
a) For each sample, predict how many votes “Journey” received.
Sample 1
Sample 2
Sample 3
b) Describe the variation in the predictions.
c) Make an inference about the number of students voting for “Journey”.
Chapter 8 – Section 4 – Data Variability
Box Plot: use ___ points on a number line to summarize a data set, the box shows the middle _______ of
the data.
Interquartile Range: (IQR) the _________________ between the upper and lower quartiles
What is the IQR of the box plot above?
Variability: tells how much a data set is spread out
Mean Absolute Deviation: (MAD) the average distance between the mean and each data value.
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Comparing Two Populations
1) A veterinarian collects data about the weights of the dogs she treats.
a) Compare the IQRs of the data sets to draw an inference about the dogs.
Australian Terrier: ________________
Boston Terrier: ________________
b) Compare the medians of the data sets to draw another inference about the dogs.
Australian Terrier: ________________
Boston Terrier: ________________
Determining Overlap of Data Sets
2) The data table below shows the number of points scored by each player on two basketball teams during
a game. Use measures of center and variability to express the amount of overlap between the data sets.
a) Calculate the mean of each data set.
Eagles:
Vikings:
b) Determine the MAD of each data set.
c) What multiple n of the MAD equals the difference between the means?
d) What does this number tell you about the overlap of the data set?
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3) The data table below shows the number of commercials during a random sample of hour-long shows on
two television stations.
a) Calculate the mean of each data set.
Station A:
Station B:
b) Determine the MAD of each data set.
c) What multiple n of MAD equals the difference between the means?
d) What does this number tell you about the overlap of the data set?
ChallengeTwo data sets have means that are very far apart, and the MADs of the data sets are very small. What can
you conclude about the amount of overlap in the data sets?
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Closure1) Find the IQRs of the data sets.
2) The data below lists the number of holes-in-one each player on a golf team scored this season.
Team 1: 0, 0, 1, 1, 1, 2, 3, 4, 6, 7
Team 2: 0, 1, 2, 2, 2, 3, 3, 4, 5, 8
a) Determine the Mean of each data set
b) Determine the MAD of the each data set
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