Hypothesis Tests

Research Questions and Data Analysis

• Research questions are answered using data analysis.

  • Data analysis involves collecting, transforming, and modeling data to extract valuable insights and support decision-making. This process helps in identifying patterns, correlations, and trends, enabling researchers to draw meaningful conclusions.

• A sample is used to infer information about a target population.

  • When studying a large population, it is often impractical to collect data from every individual. Instead, a smaller, representative sample is selected, and data analysis is performed on this sample. The results obtained from the sample are then used to make inferences or generalizations about the entire population.

• Population vs. Sample

  • Population: The entire group of individuals, objects, or events that are of interest in a study. It is the complete set from which a sample is drawn.

  • Sample: A subset of the population that is selected for study. The sample should be representative of the population to ensure that the findings can be generalized.

Population Notation Refresher

• Sample statistics are used to estimate population parameters.

  • Population Parameters: Numerical values that describe characteristics of the entire population. Examples include population mean ($\mu$), population standard deviation ($\sigma$), and population proportion ($P$). These parameters are often unknown and are estimated using sample statistics.

  • Sample Statistics: Numerical values that describe characteristics of the sample. Examples include sample mean ($\bar{y}$), sample standard deviation ($s$), and sample proportion ($\hat{p}$). Sample statistics are used to estimate the corresponding population parameters.

  • Mean: $\bar{y}$