3.16 O: Statistical Hypothesis Testing

• The null hypothesis is the default assumption that needs to be disproved.
• Arrange the steps in statistical hypothesis testing in the correct order:

  1️⃣ Formulate null and alternative hypotheses

  2️⃣ Choose a significance level

  3️⃣ Calculate the test statistic

  4️⃣ Determine the p-value

  5️⃣ Apply the decision rule
• Lowering the significance level reduces the risk of a Type I error but increases the risk of a Type II error.

  True
• Match the key term with its definition:

  Hypothesis ↔️ A statement or claim being tested

  Null Hypothesis ↔️ The default assumption to be disproved

  Test Statistic ↔️ A calculated value for decision-making
• What is the default assumption to be disproved in statistical hypothesis testing?

  Null Hypothesis
• What is the set of values for the test statistic that lead to rejecting the null hypothesis called?

  Critical Region
• Match the key term with its definition:

  Hypothesis ↔️ A statement or claim being tested

  Null Hypothesis (H₀) ↔️ The default assumption to be disproved

  Alternative Hypothesis (H₁) ↔️ The assertion that contradicts H₀

  Significance Level ↔️ Probability of rejecting a true H₀
• What would be the null hypothesis if a researcher wants to test whether a new fertilizer increases plant growth?

  Fertilizer has no effect
• Order the following steps involved in hypothesis testing:

  1️⃣ Formulate the null and alternative hypotheses

  2️⃣ Calculate the test statistic

  3️⃣ Determine the critical region

  4️⃣ Compare the test statistic to the critical region

  5️⃣ Make a decision to reject or fail to reject the null hypothesis
• What is the primary purpose of statistical hypothesis testing?

  Reject the null hypothesis
• What is the purpose of the null hypothesis in statistical hypothesis testing?

  Testable statement
• What does a significance level of 0.05 indicate in hypothesis testing?

  5% chance of Type I error
• A Type II error occurs when you reject a true null hypothesis

  False
• What is the primary assumption of a t-test regarding the population standard deviation?

  Unknown
• What is the formula for the z-statistic?

  z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}</latex>
• What is the definition of a p-value in hypothesis testing?

  Probability of extreme data given H₀ is true
• What is the purpose of statistical hypothesis testing?

  Evaluate evidence against H₀
• What does the null hypothesis (H₀) assume about an effect or difference?

  No effect or difference
• What is the consequence of a Type I error?

  Incorrectly concluding an effect exists
• Match the error type with its definition:

  Type I Error ↔️ Rejecting H₀ when true

  Type II Error ↔️ Failing to reject H₀ when false
• In what scenario would a t-test be appropriate?

  Testing exam scores of 25 students
• The z-statistic is used when the sample size is large or the population standard deviation is known.


  True
• What does a low p-value (typically < 0.05) indicate about the null hypothesis?

  Strong evidence against H₀
• A high p-value (typically ≥ 0.05) indicates weak evidence against the null hypothesis
• What does a p-value of 0.02 suggest in a study comparing two groups?

  Groups are significantly different
• If a study finds a p-value of 0.03 and α is set to 0.05, what decision is made?

  Reject the null hypothesis
• Failing to reject the null hypothesis means there is enough evidence to support the alternative hypothesis.

  False
• Match the key term with its definition:

  Null Hypothesis (H₀) ↔️ The default assumption to disprove

  Alternative Hypothesis (H₁) ↔️ Assertion contradicting H₀
• The alternative hypothesis in hypothesis testing claims an effect or a difference.
• Statistical hypothesis testing is used to evaluate whether there is enough evidence to reject a null hypothesis.
• Match the type of hypothesis with its description:

  Null Hypothesis (H₀) ↔️ Default assumption to disprove

  Alternative Hypothesis (H₁) ↔️ Assertion contradicting H₀

  Significance Level (α) ↔️ Probability of Type I error
• The significance level is the probability of incorrectly rejecting the null hypothesis.
• The set of values for the test statistic that leads to rejecting the null hypothesis is called the critical region.
• The significance level is used to determine the critical region for the test statistic.


  True
• The test statistic is a calculated value used for decision-making in hypothesis testing.


  True
• What is statistical hypothesis testing used to evaluate?

  Evidence for hypothesis rejection
• A Type II error occurs when a true null hypothesis is rejected.

  False
• The test statistic for a t-test is called the t-statistic.
• Match the key term with its definition:

  Hypothesis ↔️ A statement or claim being tested

  Null Hypothesis (H₀) ↔️ The default assumption to be disproved

  Test Statistic ↔️ A calculated value for decision-making

  Critical Region ↔️ Values leading to null hypothesis rejection
• A Type II error occurs when a real effect is missed.