STATISTICAL HYPOTHESIS TESTING

• What is the null hypothesis denoted as?

  H0
• What is the alternative hypothesis denoted as?

  H1
• What does the significance level represent?

  Probability of incorrectly rejecting the null hypothesis
• What is a hypothesis test used for?

  To test a particular claim
• What does a sample in hypothesis testing represent?

  Inference about the population
• What is the binomial distribution denoted as?

  B(n, p)
• How would you test if a spinner is biased?

  Spin it multiple times and count outcomes
• What is the expected value of p for a fair six-sided spinner?

  $\frac{1}{6}$
• What does a one-tailed test check for?

  Change in a particular direction
• What does a two-tailed test check for?

  Change in either direction
• What is the common significance level used?

  5%
• What does the critical region represent?

  Values for which you reject the null hypothesis
• What is the acceptance region?

  Values of X not rejecting the null hypothesis
• How do you find the critical value?

  Calculate probabilities for the test statistic
• What happens if the p-value is less than the significance level?

  You reject the null hypothesis
• What does a p-value represent?

  Probability of obtaining an extreme value
• What should you always do when concluding a hypothesis test?

  Relate conclusion to the original problem
• What are the steps in conducting a hypothesis test using the binomial distribution?

  1. Set up the null and alternative hypotheses.
  2. Determine the significance level.
  3. Collect sample data and calculate the test statistic.
  4. Calculate the p-value or critical region.
  5. Compare p-value with significance level or check critical region.
  6. Draw a conclusion based on the comparison.
• What are the forms of the alternative hypothesis in hypothesis testing?

  • H1: $p > \frac{1}{6}$ (more likely)
  • H1: $p < \frac{1}{6}$ (less likely)
  • H1: $p \neq \frac{1}{6}$ (unknown direction)
• What are the implications of rejecting or not rejecting the null hypothesis?

  • Rejecting H0: Evidence suggests bias exists.
  • Not rejecting H0: Insufficient evidence of bias.