8.4 Estimating a Population Proportion

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

• 1.960

• 2.576

• 2.575

• 3.291

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

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

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

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

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

What is the purpose of estimating a population proportion?

• To make inferences about the population based on sample data.

• To calculate the exact number of individuals in a population.

• To determine the average age of individuals in a sample.

• To identify the most common characteristic of a population.

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

• 0.45

• 0.53

• 0.60

• 0.50

How does the critical value affect the confidence interval?

• It influences the range of the confidence interval according to the specified confidence level.

• It determines the sample size required for the study.

• It has no effect on the confidence interval.

• It only affects the margin of error, not the interval itself.

What does it mean if a confidence interval does not contain the true population parameter?

• It indicates that the sample may not be representative of the population.

• It suggests that the population parameter is likely to be very large.

• It means that the sample size was too small to draw any conclusions.

• It implies that the confidence level was set too low.

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

• 0.342

• 0.300

• 0.400

• 0.250

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

• Larger sample sizes result in a smaller margin of error.

• Larger sample sizes result in a larger margin of error.

• Sample size has no effect on margin of error.

• Smaller sample sizes result in a smaller margin of error.

What is the difference between a point estimate and an interval estimate?

• A point estimate provides a single value, while an interval estimate provides a range of values.

• A point estimate is always more accurate than an interval estimate.

• An interval estimate is a single value, while a point estimate is a range of values.

• Point estimates are used for small samples, while interval estimates are used for large samples.

How do you interpret a 95% confidence interval of (0.202, 0.482)?

• We are 95% confident that the true population proportion lies between 0.202 and 0.482.

• There is a 95% chance that the population proportion is between 0.202 and 0.482.

• The population proportion is exactly 0.202 or 0.482 with 95% certainty.

• We can be 95% sure that the sample mean falls within this interval.