8.4 Estimating a Population Proportion

Front

What is the critical value z_c for a 99% confidence interval?

Back

2.58

Front

What is p-hat (sample proportion) if 53 out of 100 students possess a pencil?

Back

0.53

Front

What is the point estimate, p̂, for a 95% confidence interval of (0.202, 0.482)?

Back

0.342

Front

What does a 95% confidence interval for the mean indicate?

Back

It contains the true population mean 95% of the time.

Front

How large a sample is needed to estimate a population proportion with 90% confidence and a margin of error of 5%?

Back

269

Front

Define 'confidence interval'.

Back

A range of values used to estimate the true value of a population parameter.

Front

What does a higher confidence level imply about the width of the confidence interval?

Back

A higher confidence level results in a wider confidence interval.

Front

What is the formula for calculating the sample proportion (p-hat)?

Back

p-hat = x/n, where x is the number of successes and n is the sample size.

Front

What is the relationship between sample size and margin of error in estimating a population proportion?

Back

Larger sample sizes result in a smaller margin of error.

Front

What is the significance of the critical value in confidence intervals?

Back

It determines the width of the confidence interval based on the desired confidence level.