Front

What is the formula to calculate sample size for estimating a population proportion?

Back

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

Front

What does p-hat (\u03bph) represent in statistics?

Back

p-hat (\u03bph) is the sample proportion, calculated as the number of successes divided by the total sample size.

Front

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

Back

Confidence Interval = p-hat ± Z * sqrt((p-hat * (1 - p-hat)) / n), where Z is the Z-score for the desired confidence level.

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 Z-score for a 95% confidence level?

Back

The Z-score for a 95% confidence level is approximately 1.96.

Front

If 53 out of 100 students have a pencil, what is p-hat?

Back

p-hat = 53/100 = 0.53.

Front

What is the margin of error in a confidence interval?

Back

The margin of error is the range within which the true population parameter is expected to fall, calculated as Z * standard error.

Front

How do you interpret a 95% confidence interval of 0.30 to 0.34?

Back

We are 95% confident that the true proportion of 'no' voters lies between 30% and 34%.

Front

What is the purpose of constructing a confidence interval?

Back

To estimate the range of values within which a population parameter is likely to fall, based on sample data.

Front

What does it mean if a sample size is too small?

Back

A small sample size may lead to inaccurate estimates and wider confidence intervals, reducing reliability.