Making Inferences from a Random Sample

Warm Up is on slide 2. There is no label.

Warm Up5

• Random samples can represent entire populations and support valid inferences.

• Dot plots and box plots can be used to make inferences about a population.

• Inferences or predictions about a population can be made using data based on a random sample, along with proportional reasoning.

A baker selects 25 trays of cupcakes and finds 3 trays that

have cupcakes with too little icing. If the bakery made 125 trays of

cupcakes, how many trays can the baker expect to have cupcakes with

too little icing inthem? Explain how you found your

answer.

How can you use a sample to make inferences about a population?

If the sample is random, you can write a proportion that relates the

number of items in the sample with a certain trait to the number

of items in the population with the same trait.

How do you find the median of a set of numbers?

Write the numbers in order from least to greatest. If there is an odd number

of values, the median is the middle value in the list. If there is an even number of values, there will be two middle values and the median is the

average of these two numbers.

What is the difference between the median and the mean for a set of

numbers?

The median is the middle value when the set of numbers is written

in order. The mean is found by dividing the sum of all the values in the set by the number of values in

the set.

Can random samples and proportional reasoning be used to determine precise

information about a population?

No, random samples and proportional reasoning can only be used to make predictions. While these predictions

are likely to be close to the actual value, it is possible for a prediction to

be inaccurate.

A band has sold out a concert with4,200 seats. A random sample of120 ticket buyers is surveyed, and28 buyers made their purchase on

the first day tickets were being sold. How many of the 4,200 tickets are

likely to have been purchased on thefirst day they were available?

A manufacturer fills an order for 4,200 smart phones. The quality

inspector selects a random sample of 60 phones and finds that 4 are

defective. How many smart phones in the order are likely to be

defective?

Scientists often use random samples to estimate the size of an animal population.

For example, to estimate the size of a population of deer, scientists can capture a random sample of 100 deer and place an

identifying mark on each deer’s left ear. All 100 deer are then released back into the

wild. A month later, another sample of 50 deer is captured. If 4 deer in this sample

already have the identifying mark on their left ear, how large is the deer population?

Exit Ticket1. A random sample of 25 of the 400 members of the Bigtime

Theater Company is surveyed about how many plays each has acted in. Make a box plot of the data. Then make a qualitative statement about the population. 3, 5, 5, 3, 4, 4, 1, 3, 6, 10, 1, 3, 4, 5, 1, 2, 4, 2, 3, 2, 5, 5, 5, 5, 6

2. Gerald buys a bag of 7,500 assorted beads online. A random sample of 150 beads contains 17 red beads. Predict the number of red beads in the bag of assorted beads that Gerald bought.

3. A store manager selects 30 cartons of eggs and finds 4 cartons that have cracked eggs. If the store has 105 cartons of eggs, how many cartons can she expect to have cracked eggs in them?

4. Jon finds a box of 350 postcards. He selects a random sample of 75 postcards and finds that 27 already have a stamp on them. Predict the total number of postcards in the box with stamps on them.