2.1 Estimation

• Statistical inference is the process of drawing conclusions about a population
• The two main types of statistical inference are point estimation and interval estimation.
• Match the type of inference with its key components:

  Point Estimation ↔️ Single value estimate

  Interval Estimation ↔️ Range of values
• Statistical inference involves using statistical methods to infer properties of the population
• Estimating the average height of a population by calculating the average height of a random sample is an example of statistical inference.
• Order the steps in the process of statistical estimation:

  1️⃣ Collect a sample

  2️⃣ Calculate sample statistics

  3️⃣ Determine the type of estimation (point or interval)

  4️⃣ Provide a point estimate or construct a confidence interval
• Point estimation provides a single number
• Interval estimation provides a range of values along with a confidence level.
• Point estimation provides a single value for a population parameter
• An unbiased estimator has an expected value equal to the true population parameter.
• Efficiency refers to an estimator with the smallest variance
• Consistency means that the estimator converges to the true population parameter as the sample size increases.
• Match the property of an estimator with its definition:

  Unbiasedness ↔️ Expected value equals true parameter

  Efficiency ↔️ Smallest variance among unbiased estimators

  Consistency ↔️ Converges to true parameter as sample size increases
• What does interval estimation provide as output?

  A confidence interval
• Estimation is the process of determining approximate values for population parameters based on sample statistics
• Point estimation provides a single value as the best estimate of a population parameter.
• What does interval estimation include in its output besides a range of values?

  A confidence level
• Point Estimation provides a single value as the best guess for a population parameter
• Match the type of estimation with its output:

  Point Estimation ↔️ Single value

  Interval Estimation ↔️ Range with confidence level
• Unbiasedness means the expected value of the estimator equals the true population parameter.
• Which property of an estimator indicates the smallest variance among all unbiased estimators?

  Efficiency
• An estimator is consistent if it converges to the true population parameter as the sample size increases
• A point estimator is a single value based on sample data used to estimate a population parameter.
• What is the formula for the sample mean?

  \(\bar{x} = \frac{1}{n} \sum_{i = 1}^{n} x_{i}\)</latex>
• The formula for the sample variance is \(s^{2} = \frac{1}{n - 1} \sum_{i = 1}^{n} (x_{i} - \bar{x})^{2}\), where \(\bar{x}\) is the sample mean
• To construct a confidence interval, you combine sample data with a desired confidence level.
• What does the standard error measure in a confidence interval?

  Standard deviation of the sample mean
• The critical value in a confidence interval is obtained from standard normal distribution tables
• The confidence interval for a population parameter is calculated as \(\bar{x} \pm z_{\alpha / 2} \cdot SE\).
• What is the goal of statistical inference?

  Draw conclusions about a population
• What is the output of point estimation?

  Single value
• Interval Estimation provides a range within which the population parameter is likely to lie, along with a confidence level
• Point estimation estimates a population parameter with a single number
• Interval estimation provides a range within which a population parameter is likely to lie, along with a confidence level.
• Match the type of estimation with its output:

  Point Estimation ↔️ Single value

  Interval Estimation ↔️ Range with confidence level
• What is the definition of unbiasedness in estimators?

  Expected value equals parameter
• An estimator is efficient if it has the smallest variance
• Consistency of an estimator means it converges to the true population parameter as the sample size increases.
• Order the steps to calculate point estimators using sample data:

  1️⃣ Calculate the sample mean

  2️⃣ Determine the sample median

  3️⃣ Compute the sample variance
• The formula for the sample mean is \(\bar{x} = \frac{1}{n} \sum_{i = 1}^{n} x_{i}\), where n represents the sample size