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Hypothesis Testing Concepts in Business Statistics

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  • Alpha
    Alpha is the probability of rejecting the null hypothesis when it is actually true.
  • Alternative hypothesis (H1)
    The hypothesis that represents the opposite of the null hypothesis and states the population parameter is <, >, or ≠ a specific value.
  • Beta
    Beta is the probability of failing to reject the null hypothesis when it is actually false.
  • Consumer’s risk
    A Type II error in quality control where the customer receives a product from a faulty process.
  • Critical sample mean, Xalpha
    The sample mean that marks the boundary of the rejection region in hypothesis testing.
  • Critical sample proportion, p-alpha
    The sample proportion that marks the boundary of the rejection region when testing a population proportion.
  • Hypothesis
    An assumption about a population parameter such as a mean or proportion.
  • Level of significance
    The probability of making a Type I error, denoted by alpha.
  • Null hypothesis (H0)
    The status quo hypothesis stating the population parameter is ≤, =, or ≥ a specific value, always including equality.
  • Observed level of significance (p-value)
    The probability of observing a sample mean at least as extreme as the one selected, assuming the null hypothesis is true.
  • One-tailed hypothesis test
    A test where the alternative hypothesis is stated as either < or >.
  • One-tail (lower) hypothesis test
    A test where the alternative hypothesis is stated as <.
  • One-tail (upper) hypothesis test
    A test where the alternative hypothesis is stated as >.
  • P-value
    The probability of observing a sample mean at least as extreme as the one selected, assuming the null hypothesis is true.
  • Power
    The probability that a hypothesis test correctly rejects the null hypothesis.
  • Power Curve
    A curve plotting the power values of a hypothesis test over a range of population means.
  • Producer’s risk
    A Type I error in quality control where the producer detects a problem in the process that does not exist.
  • Two-tail hypothesis test
    A test where the alternative hypothesis is stated as not equal (≠).
  • Type I error
    Rejecting the null hypothesis when it is actually true; probability is alpha.
  • Type II error
    Failing to reject the null hypothesis when it is actually false; probability is beta.