hypothesis testing

• Greater Than (>): 1 tail

  • “Exceeds”
  • “More than”
  • “Higher than”
  • “Surpasses”
  • “Above”
• Less Than (<): 1 tail

  • “Below”
  • “Under”
  • “Lower than”
  • “Fewer than”
  • “Short of”
• Not Equal (≠): 2 tail

  • “Varies from”
  • “Is different from”
  • “Does not match”
  • “Is not the same as”
  • “Diverges from”
• 1. Hypothesis Testing: It is a statistical method that is used to decide whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population.
• Levels of Significance: This is a threshold below which the p-value of the test statistic must fall in order for us to reject the null hypothesis. It’s often denoted by the Greek letter alpha (α) and represents the probability of making a Type I error, which is rejecting a true null hypothesis2.

  1. Critical Value: This is the value that separates the region where the null hypothesis is not rejected from the region where the null hypothesis can be rejected with confidence. It’s determined by the test statistic’s distribution and the significance level
• Degree of Freedom: Often abbreviated as df, this term refers to the number of independent values or quantities which can vary in an analysis without violating any given constraints. It’s typically calculated as the sample size minus the number of parameters estimated
• test statistic is a value calculated from a sample of data and used in a hypothesis test. It helps determine how closely the observed data match the expected distribution under the null hypothesis. The test statistic is used to calculate the p-value, which in turn helps to decide whether to reject the null hypothesis
• • Confidence Level: The percentage of times that a confidence interval, constructed in the same way from the same population, would contain the true parameter value
• Critical Value:

  • Rejection Region: The range of values for which the null hypothesis is not considered plausible and is rejected
• • Acceptance Region: The range of values for which the null hypothesis is considered plausible and is not rejected
• • Z value: A type of critical value that corresponds to the standard normal distribution.
• • Sample Size (n): The number of observations in a sample, which is used in the calculation of degrees of freedom.
• • Estimated Parameters: The number of parameters estimated in the model, which are subtracted from the sample size to calculate degrees of freedom.
• • Z Statistic: A test statistic used when the sample size is large and the population variance is known, following a standard normal distribution.
• • T Statistic: A test statistic used when the sample size is small or the population variance is unknown, following a Student’s t-distribution.