(206) AP Statistics: Topic 6.2 Constructing a Confidence Interval for a Population Proportion

What is a population proportion?

The true proportion of all individuals in an entire population that fit into a described category.

What is a point estimate?

A sample proportion (denoted as P hat) used as an estimate for a population proportion.

What does an interval represent in statistics?

A range of values that represent what the true population parameter could be.

What is a sampling distribution?

The distribution of all possible sample proportions from repeated random sampling from a population.

What is deductive reasoning?

Reasoning that starts with known truths and seeks evidence to support those truths.

What is the alpha level?

The percentage of samples in any sampling distribution that are considered significant.

What is a critical value (Z star)?

A special z-score that represents the cutoff for significant samples in a sampling distribution.

What is standard error?

An estimate of the standard deviation of the sampling distribution, calculated using the sample proportion (P hat) instead of the population proportion (P).

What is the formula for a one-sample Z interval for a proportion?

P hat ± Z star * SE, where SE is the standard error.

What are the four steps to find a confidence interval?

1. Name the interval; 2) Check conditions; 3) Use the formula; 4) Provide a conclusion in context.

What does it mean to be 98% confident in a sample proportion?

It means that we expect the true population proportion to fall within a specified interval 98% of the time.

How do you calculate margin of error?

The margin of error is calculated as Z star times the standard error.

What is the condition for using the normal model for sampling distributions?

The sample size must be large enough, typically at least 10 successes and 10 failures.

What should you do if you don't know the true population proportion?

Use inductive reasoning to gather sample evidence to estimate the population proportion.

What is the significance of a critical Z star of 1.9600?

It indicates the cutoff for the top and bottom 2.5% in a 95% confidence level.

What is indicated by a sampling distribution showing that 98% of P hats are normal?

That only 2% of samples are considered significant, being either extremely high or low.