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 Sample1) 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 Questions3) 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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Challenge-A 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?

Closure-Is 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 Ringer-1) 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 t hat aremarkedtotal number counted = total numbermarkedestimated population

Using the Capture/Recapture Method-1) 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?

Challenge-In a capture/recapture program, 30% of the animals recaptured have tags. Suppose 70 animals were originally captured, tagged and released. Estimate the population.

ClosureUse a proportion to estimate the population of each.

1) Total bison counted: 350 2) Total elk counted: 675 Tagged bison counted: 45 Marked elk counted: 123 Total tagged bison: 100 Total marked elk: 465

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Bell Ringer- Use a proportion to estimate each animal population.

1) Total Trout Counted: 4,000 2) Total Rabbits Counted: 685 Tagged Trout Counted: 350 Tagged Rabbits Counted: 235 Total Tagged Trout: 2,500 Total Tagged Rabbits: 550

Chapter 8 – Section 3 – Inferences

Inference: a ________________ or conclusion based on data or reasoning

Drawing Inferences about a Population1) 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 Samples3) 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∈the samplenumber of students∈the sample

= predicted votes for Carlosnumber of students∈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.

ChallengeA 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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Closure1) 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 Ringer-1) 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.8

Comparing Two Populations1) 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 Sets2) 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?

Challenge-Two 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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Closure-1) 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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