Confidence Interval - Minimum Sample Size

How do you calculate the standard error of the mean?

• SEM = σ / √n

• SEM = n / σ

• SEM = σ * n

• SEM = σ + n

What is the formula for calculating the minimum sample size for estimating a population mean?

• n = (Z^2 * σ^2) / E^2

• n = (E^2 * Z) / σ^2

• n = (Z * σ) / E

• n = (σ^2 * E) / Z^2

What is the Z-value for a 95% confidence level?

• 1.64

• 1.96

• 2.58

• 1.75

What is the formula for calculating the minimum sample size for estimating a population proportion?

• n = (Z^2 * p * (1-p)) / E^2

• n = (Z * p) / E

• n = (Z^2 * p) / (1-p)

• n = (E^2 * p * (1-p)) / Z^2

What is the relationship between sample size and the precision of an estimate?

• Larger sample sizes generally lead to more precise estimates, resulting in narrower confidence intervals and a higher likelihood of capturing the true population parameter.

• Smaller sample sizes provide more precise estimates due to reduced variability.

• Sample size has no effect on the precision of an estimate.

• Larger sample sizes lead to less precise estimates because of increased variability.

If a researcher wants to estimate a proportion with a margin of error of 0.05 and a confidence level of 95%, what is the impact of increasing the margin of error on the required sample size?

• Increasing the margin of error will decrease the required sample size, as a larger margin allows for a less precise estimate.

• Increasing the margin of error will increase the required sample size, as a larger margin requires more precision.

• Increasing the margin of error has no effect on the required sample size.

• Increasing the margin of error will make the sample size irrelevant.

What is the margin of error in the context of confidence intervals?

• The margin of error is the range within which the true population parameter is expected to lie, given a certain level of confidence. It is calculated as the product of the Z-value and the standard error.

• The margin of error is the maximum amount that the sample results can differ from the true population parameter.

• The margin of error is a statistical term that describes the likelihood that a sample accurately reflects the population.

• The margin of error is the difference between the highest and lowest values in a data set.

What is the significance of conducting a pilot study before determining sample size?

• A pilot study is used to test the research hypothesis before the main study.

• A pilot study helps estimate parameters such as the proportion or standard deviation, which are essential for calculating the required sample size for the main study.

• A pilot study is conducted to finalize the research design and methodology.

• A pilot study is primarily used to recruit participants for the main study.

What is a confidence interval?

• A method to calculate the mean of a data set.

• A range of values likely to contain the true value of an unknown population parameter.

• A statistical test to determine the significance of results.

• A graphical representation of data distribution.

How does the population standard deviation influence sample size calculations?

• A larger population standard deviation requires a larger sample size to achieve the same level of precision in estimating the population parameter.

• A larger population standard deviation allows for a smaller sample size to achieve the same level of precision.

• The population standard deviation has no effect on sample size calculations.

• A smaller population standard deviation requires a larger sample size to achieve the same level of precision.