8.4 Estimating a Population Proportion

Front

What is p-hat in statistics?

Back

p-hat (p̂) is the sample proportion, calculated as the number of successes (e.g., individuals with a certain characteristic) divided by the total number of observations in the sample.

Front

How do you calculate the standard error of a sample proportion?

Back

The standard error (SE) of a sample proportion is calculated using the formula: SE = sqrt[(p̂(1 - p̂)) / n], where p̂ is the sample proportion and n is the sample size.

Front

What does a confidence interval represent in statistics?

Back

A confidence interval provides a range of values that is likely to contain the true population parameter with a specified level of confidence (e.g., 95%).

Front

What is the purpose of a confidence interval?

Back

To estimate the range within which the true population parameter lies with a certain level of confidence.

Front

If a 95% confidence interval is (0.202, 0.482), what is the point estimate p̂?

Back

The point estimate p̂ is the midpoint of the confidence interval, calculated as (0.202 + 0.482) / 2 = 0.342.

Front

What is the formula for calculating p-hat?

Back

p-hat = (number of successes) / (total number of observations).

Front

What does a standard error of 0.016 indicate?

Back

A standard error of 0.016 indicates the variability of the sample proportion estimate; smaller values suggest more precise estimates.

Front

What is the significance of the shaded area in a confidence interval?

Back

The shaded area represents the level of significance; for example, if each shaded area is 0.05, the confidence level is 90%.

Front

What is the relationship between sample size and standard error?

Back

As the sample size increases, the standard error decreases, leading to more precise estimates of the population proportion.

Front

What does a 90% confidence level mean?

Back

A 90% confidence level means that if we were to take many samples and construct confidence intervals, approximately 90% of those intervals would contain the true population parameter.