Making Inferences from a Random Sample

1. Making Inferences from a Random Sample Warm Up is on slide 2. There is no label.

2. Warm Up 5

3. 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.

4. 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.

5. 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.

6. 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 theaverage of these two numbers.

7. 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.

8. 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.

9. A band has sold out a concert with4,200 seats. A random sample of120 ticket buyers is surveyed, and28 buyers made their purchase onthe first day tickets were being sold. How many of the 4,200 tickets arelikely to have been purchased on thefirst day they were available?

10. 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?

11. 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?

12. Exit Ticket • 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 • 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. • 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? • 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.