Margin of Error and Confidence Intervals

​I can interpret the margin of error.
I can use data from samples to predict population proportions and means.
I can analyze a data set to determine whteher or not it cantains messy data. I can use confidence intervals to determine the margin of error.

A Vote of Confidence

Vocabulary

Margin of error

the maximum expected difference between the true population data and the sample estimate of the data.

Multiple Choice

In a poll of 1100 registered voters before a mayoral election, 594 people (54%) said they would vote for the current mayor. The margin of error was ±3%, which means the poll predicts that between 51% (54-3) and 57% (51+3) of people will actually vote for the sitting mayor.

Which does the poll represent?

• A sample survey

• An observational survey

• An experiment

• Schrodinger's cat

Multiple Select

In a poll of 1100 registered voters before a mayoral election, 594 people (54%) said they would vote for the current mayor. The margin of error was ±3%, which means the poll predicts that between 51% (54-3) and 57% (51+3) of people will actually vote for the sitting mayor.

Can you conclude that the current mayor will be reelected?

• The results suggest that the mayor will win because the range is more than 50%.

• However, the actual results could be different.

• The people who responded could change their minds or not vote.

• The people who answered might have been dishonest.

Open Ended

In a poll of 1100 registered voters before a mayoral election, 594 people (54%) said they would vote for the current mayor. The margin of error was ±3%, which means the poll predicts that between 51% (54-3) and 57% (51+3) of people will actually vote for the sitting mayor.

Is it possible for fewer than 50% of respondents in a new sample to respond that they will vote for the mayor in the election? It is likely?

​Proportion of individuals in a population sharing a certain trait, denoted p

​​Population Proportion

​proportion of individuals in a sample sharing a certain trait

​​Sample Proportion

​The set of sample proportions for all possible equal-sized sample. A display will have the number of samples along the vertical axis. It will be close to a normal distribution.

​​Sampling Distribution

​Confidence Intervals

An estimated range of values the likely include the population proportion or population mean.

When stating the margin of error, we typically use a 95% confidence interval. We use the sample proportion and the standard deviation do the sampling distribution.

​Confidence Intervals

• The lower bound of a 68% CI ranges from 1 standard deviation below to 1 standard deviation above the sample proportion.

• The lower bound of a 95% CI ranges from 2 standard deviaions below to 2 standard deviations above.

• The lower bound of a 99.7% CI ranges from 3 standard deviations below to 3 standard deviations above.

Multiple Choice

In a poll of 1100 registered voters before a mayoral election, 594 people (54%) said they would vote for the current mayor. The margin of error was ±3%, which means the poll predicts that between 51% (54-3) and 57% (51+3) of people will actually vote for the sitting mayor.

What is the confidence interval for 68%?

• The interval between 52.5% and 55.5%.

• The interval between 51.0% and 57.0%

• The interval between 49.5% and 58.5%.

• The interval between 25% and 75%.

Multiple Choice

In a poll of 1100 registered voters before a mayoral election, 594 people (54%) said they would vote for the current mayor. The margin of error was ±3%, which means the poll predicts that between 51% (54-3) and 57% (51+3) of people will actually vote for the sitting mayor.

What is the confidence interval for 95%?

• The interval between 52.5% and 55.5%.

• The interval between 51.0% and 57.0%

• The interval between 49.5% and 58.5%.

• The interval between 25% and 75%.

Multiple Choice

In a poll of 1100 registered voters before a mayoral election, 594 people (54%) said they would vote for the current mayor. The margin of error was ±3%, which means the poll predicts that between 51% (54-3) and 57% (51+3) of people will actually vote for the sitting mayor.

What is the confidence interval for 99.7%?

• The interval between 52.5% and 55.5%.

• The interval between 51.0% and 57.0%

• The interval between 49.5% and 58.5%.

• The interval between 25% and 75%.

Open Ended

In a poll of 1100 registered voters before a mayoral election, 594 people (54%) said they would vote for the current mayor. The margin of error was ±3%, which means the poll predicts that between 51% (54-3) and 57% (51+3) of people will actually vote for the sitting mayor.

Explain the similarities and differences between each CI for the election poll.

Open Ended

Use a 95% confidence interval to deter the margin of error and range of value for the following population proportion.

A survey of 1500 teenagers shows that 83% do not like waking up early in the morning.

Open Ended

Use a 95% confidence interval to deter the margin of error and range of value for the following population proportion.

A survey of 200 licensed high school students shows that 16% onw their own car.

Open Ended

Use a 95% confidence interval to deter the margin of error and range of value for the following population proportion.

A survey of 500 high school students says, "90% say math is their favorite class."