Math 4 Unit 7 Review - Statistical Inference

Front

What is the formula to determine the sample size needed for estimating a population proportion with a specified confidence level and margin of error?

Back

n = (Z^2 * p̂ * (1 - p̂)) / E^2, where Z is the Z-score for the confidence level, p̂ is the estimated proportion, and E is the margin of error.

Front

What does the symbol p̂ represent in statistics?

Back

p̂ represents the sample proportion.

Front

What is a point estimate in statistics?

Back

A point estimate is a single value estimate of a population parameter, such as the sample mean.

Front

What factors affect the width of a confidence interval?

Back

The width of a confidence interval is affected by the sample size, the sample standard deviation, and the critical value (t* or Z), but not the sample mean.

Front

How do you calculate a 95% confidence interval for a population proportion?

Back

The formula is: CI = p̂ ± Z * sqrt[(p̂(1 - p̂) / n)], where Z is the Z-score for 95% confidence.

Front

What is the Z-score for a 90% confidence level?

Back

The Z-score for a 90% confidence level is approximately 1.645.

Front

What is the standard deviation of the sample mean (standard error)?

Back

Standard error (SE) = σ / sqrt(n), where σ is the population standard deviation and n is the sample size.

Front

What is the difference between a sample and a population?

Back

A sample is a subset of a population used to represent the whole, while a population includes all members of a specified group.

Front

What is the purpose of constructing a confidence interval?

Back

The purpose of constructing a confidence interval is to estimate a population parameter with a specified level of confidence.

Front

What does a 95% confidence interval mean?

Back

A 95% confidence interval means that if we were to take many samples and construct intervals, approximately 95% of those intervals would contain the true population parameter.