2.5 Statistical Hypothesis Testing

• The null hypothesis (H0) represents the status quo or no change
• What is the goal of statistical hypothesis testing?

  Reject or fail to reject H0
• Order the types of one-tailed tests based on their direction:

  1️⃣ Left-Tailed (H1: μ < value)

  2️⃣ Right-Tailed (H1: μ > value)
• Match the type of test with its alternative hypothesis:

  One-Tailed (Left) ↔️ μ < value

  One-Tailed (Right) ↔️ μ > value

  Two-Tailed ↔️ μ ≠ value
• What are the two types of alternative hypotheses based on directionality?

  One-sided and two-sided
• The alternative hypothesis can be one-sided or two-sided.


  True
• In a two-tailed test, the alternative hypothesis specifies that the population mean is different from the value stated in H0, without specifying a direction
• In a one-tailed left test, the alternative hypothesis is μ < value.


  True
• What does the p-value represent in hypothesis testing?

  Probability of observing data if H0 is true
• What does the null hypothesis (H0) represent in statistical hypothesis testing?

  Status quo or no change
• What is specified in the alternative hypothesis of a two-tailed test?

  Population mean is different
• What is the purpose of the significance level (α) in hypothesis testing?

  Threshold for rejecting H0
• What is the common range for the significance level (α) in hypothesis testing?

  0.05 or 0.01
• For what type of data is the Chi-Squared (χ²) Test used?

  Categorical data
• Steps involved in conducting a hypothesis test

  1️⃣ State the null (H0) and alternative (H1) hypotheses

  2️⃣ Choose a significance level (α)

  3️⃣ Determine the appropriate statistical test

  4️⃣ Calculate the test statistic and p-value

  5️⃣ Compare the p-value to α and make a decision
• If the p-value is less than or equal to α, we reject the null hypothesis.


  True
• The alternative hypothesis (H1) contradicts the null hypothesis.


  True
• There are two types of hypothesis tests based on the directionality of the alternative hypothesis: one-tailed and two-tailed
• The null hypothesis must be specific and testable.

  True
• Order the types of hypothesis tests based on their critical regions:

  1️⃣ One-Tailed (Left): Left tail

  2️⃣ One-Tailed (Right): Right tail

  3️⃣ Two-Tailed: Both tails
• What type of hypothesis test is used when testing if the average height of students is greater than 170 cm or less than 170 cm?

  One-tailed test
• In a two-tailed test, the alternative hypothesis is μ ≠
• If the p-value is less than or equal to α, we reject the null hypothesis.


  True
• What does the alternative hypothesis (H1) contradict in hypothesis testing?

  Null hypothesis (H0)
• What is the significance level (α) in hypothesis testing?

  Probability of rejecting H0 when true
• If the p-value is less than or equal to α, we reject the null hypothesis.


  True
• If α = 0.05 and the p-value = 0.03, we reject the null hypothesis.


  True
• The z-test is used when the population standard deviation is known
• Use the z-test when the population standard deviation is known and you want to test the population mean
• What is the software's role in calculating the test statistic and p-value?

  Automation
• What does it mean if a test with α = 0.05 produces a p-value of 0.03?

  Reject H0; strong evidence for H1
• What are the two types of hypotheses defined in statistical hypothesis testing?

  Null and alternative
• Match the description with the corresponding hypothesis:

  Null Hypothesis (H0) ↔️ States that there is no significant difference

  Alternative Hypothesis (H1) ↔️ States that there is a significant difference
• What does the alternative hypothesis specify in a two-tailed test?

  μ ≠ value
• The null hypothesis states that there is no significant difference or change
• What does a one-tailed test specify about the direction of change?

  Either greater than or less than
• What are the two types of hypothesis tests based on the directionality of the alternative hypothesis?

  One-tailed and two-tailed
• What is the significance level (α) in hypothesis testing?

  Probability of rejecting true H0
• If α = 0.05 and the p-value is 0.03, we reject
• The alternative hypothesis can be one-sided or two-sided