Module 9 Practice Questions

Front

What is a confidence interval?

Back

A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter. It is used to estimate the uncertainty around a sample statistic.

Front

What does it mean for a sample to be random?

Back

A random sample is one in which every member of the population has an equal chance of being selected. This helps to ensure that the sample is representative of the population.

Front

What is the sample proportion (p̂)?

Back

The sample proportion (p̂) is the ratio of the number of successes in a sample to the total number of observations in that sample. It is used as an estimator for the population proportion (p).

Front

What is the relationship between sample size and the accuracy of the sample proportion?

Back

As the sample size increases, the sample proportion is expected to be closer to the population proportion, reducing the margin of error.

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What is an unbiased estimator?

Back

An unbiased estimator is a statistic that, on average, equals the parameter it estimates. For example, the sample proportion (p̂) is an unbiased estimator of the population proportion (p).

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What is the margin of error in polling?

Back

The margin of error is a statistic that expresses the amount of random sampling error in a survey's results. It indicates the range within which the true population parameter is expected to fall.

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How do you calculate the sample size needed for a given margin of error?

Back

The sample size (n) can be calculated using the formula: n = (Z^2 * p̂ * (1 - p̂)) / E^2, where Z is the Z-score corresponding to the desired confidence level, p̂ is the estimated proportion, and E is the margin of error.

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What is the significance of a 95% confidence level?

Back

A 95% confidence level means that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 95 of the intervals would contain the true population parameter.

Front

What is the formula for a confidence interval for a proportion?

Back

The confidence interval for a proportion is calculated as: p̂ ± Z * sqrt[(p̂(1 - p̂) / n)], where p̂ is the sample proportion, Z is the Z-score for the desired confidence level, and n is the sample size.