Lesson 11.5 Interpreting Data Essential Question: How do you make conclusions about populations using surveys?

Before we start… If you knew that 15% of the students in your math class supported a field trip, how could you relate this information to the number of students in the entire school who might support the trip?

Making Population Predictions If you know the size of a sample and the responses, you can make predictions about the entire population.

Television networks rely on surveys to determine how many people watch their programs. There are about 105 million households in the United States. In a survey of 5000 randomly selected American households, 780 of the households watched the program. How many households in the United States watch the program?

Television networks rely on surveys to determine how many people watch their programs. There are about 105 million households in the United States. In a survey of 5000 randomly selected American households, 460 of the households watched the program. How many households in the United States watch the program?

In a random survey of 100,000 adult residents of a city with an adult population of 1.5 million, 65,800 are in favor of a new shopping mall. Of all the adult residents of the city, how many are in favor of the new mall?

Margin of Error When a survey samples only a portion of a population, different surveys of the same population may have different results. Due to such variation, a survey should include a margin of error.

What is a margin of error? An interval centered on a sample percent in which a population percent is most likely to lie. A sample percent of 32% with a margin of error ±5% means that the population percent is most likely between 27% and 37%.

A survey of a random sample of voters predicts that candidate A will receive 52% of the votes and that candidate B will receive 48% of the votes. The margin of error is ±3%. Can you predict who will win the election?

The mayor of a city is running for re-election The mayor of a city is running for re-election. A survey of some city residents predicts that the mayor will receive 58% of the votes from likely voters and her challenger will receive 42% of the votes. The margin of error for the survey is ±5%. Can you predict who will win the election?

A survey of a random sample of voters predicts that candidate A will receive 53% of the votes and that candidate B will receive 47% of the votes. The margin of error is ±4%. Can you predict who will win the election?

A survey of a random sample of voters predicts that candidate A will receive 54% of the votes and that candidate B will receive 46% of the votes. The margin of error is ±3%. Can you predict who will win the election?

A survey claims that between 41% and 53% of voters are likely to vote against a new proposition. What is the margin of error for the survey?

How do you make conclusions about populations using surveys? When reading the results of a survey, consider the following: What is the population and the sampling method Does the sample represent the population Are the survey questions biased What’s the margin of error Are the data displays potentially misleading Are the conclusions supported by the data

Tell what conclusions you can make from the following newspaper article.

Tell what conclusions you can make from the following newspaper article.

Tell what conclusions you can make from the following report. Recently, researchers surveyed 1000 patrons of a local shopping mall and asked them if they were “strongly for”, “mildly for” or “against” the city’s plans to buy some residents’ houses and demolish them to make room for a new upscale mall. Most residents – 780 out of 1000 – were for having the new mall.

How do you make conclusions about populations using surveys?

Ticket Out the Door A survey of 200 randomly selected dog owners finds that 130 dog owners prefer brand A dog food. Predict how many owners in a town of 1500 dog owners prefer brand A dog food.