2.5 Statistical Hypothesis Testing

• In statistical hypothesis testing, we set up two key hypotheses: the null hypothesis and the alternative
• The null hypothesis represents the status quo or no change.


  True
• Common significance levels are 5% and 1%.

  True
• What does a one-tailed test examine in hypothesis testing?

  Change in a specific direction
• One-tailed tests are more powerful when the alternative hypothesis is correct
• The alternative hypothesis in a one-tailed test specifies the direction
• The null hypothesis assumes there is no effect
• A Type I error occurs when the null hypothesis is rejected but is actually true
• Match the test statistic with its use:

  t-statistic ↔️ Population standard deviation unknown, small sample

  z-statistic ↔️ Population standard deviation known, large sample
• Critical values are determined based on the chosen significance level and whether the test is one-tailed or two-tailed
• The critical value is the threshold the test statistic must exceed to reject the null hypothesis.


  True
• For a two-tailed t-test with α = 0.05 and n = 20, the critical value is found using 19 degrees of freedom.


  True
• Match the test type with its significance level and critical value condition:

  One-Tailed, α = 0.01 ↔️ Area to the right of critical value = 0.01

  Two-Tailed, α = 0.05 ↔️ Area to the right of critical value = 0.025

  One-Tailed, α = 0.05 ↔️ Area to the right of critical value = 0.05

  Two-Tailed, α = 0.01 ↔️ Area to the right of critical value = 0.005
• Steps to decide whether to reject the null hypothesis:

  1️⃣ Calculate the test statistic

  2️⃣ Determine the critical value

  3️⃣ Compare the test statistic to the critical value

  4️⃣ Reject or fail to reject the null hypothesis
• Match the hypothesis with its definition:

  Null Hypothesis (H₀) ↔️ Statement to be disproven

  Alternative Hypothesis (H₁) ↔️ Statement accepted if H₀ is rejected
• Match the error type with its description:

  Type I Error ↔️ Rejecting H₀ when it is true

  Type II Error ↔️ Failing to reject H₀ when it is false
• What is the alternative hypothesis in a one-tailed test for an increase in blood pressure?

  H₁: μ > 120 mmHg
• The t-statistic formula includes the sample mean, hypothesized population mean, sample standard deviation, and sample size
• What is a test statistic used for in statistical hypothesis testing?

  To reject the null hypothesis
• Match the symbols with their meanings in the t-statistic formula:

  $\bar{x}$ ↔️ Sample mean

  $\mu_{0}$ ↔️ Hypothesized population mean

  $s$ ↔️ Sample standard deviation

  $n$ ↔️ Sample size
• The formula for the z-statistic is $z =$$\frac{\bar{x} - \mu_{0}}{\sigma / \sqrt{n}}$
• In a one-tailed test with α = 0.05, the critical value is the value from the t-distribution or z-distribution with area to the right of the critical value equal to $\alpha$
• If the test statistic exceeds the critical value, we reject the null hypothesis

  True
• What does a lower significance level reduce the chance of?

  Type I error
• A lower significance level increases the chance of a Type II error.


  True
• If the test statistic does not exceed the critical value, we fail to reject the null hypothesis.


  True
• The null hypothesis represents the status quo or no effect.


  True
• One-tailed tests are more powerful when the alternative hypothesis is correct
• The alternative hypothesis in a one-tailed test specifies the direction of the change.


  True
• One-tailed tests are more powerful than two-tailed tests when the alternative hypothesis is correct.

  True
• Two-tailed tests are appropriate when the direction of the effect is unknown.

  True
• The formula for the t-statistic is $t =$$\frac{\bar{x} - \mu_{0}}{s / \sqrt{n}}$.


  True
• What is the critical value in statistical hypothesis testing?

  Threshold to reject H₀
• What area to the right of the critical value is used in a two-tailed test with α = 0.05?

  α/2
• What is the next step after calculating the test statistic in hypothesis testing?

  Compare to critical value
• How is the critical value determined for a two-tailed test with a significance level of 5%?

  Area to the right of α/2
• What decision is made if the test statistic exceeds the critical value in a hypothesis test?

  Reject the null hypothesis
• For a two-tailed test with a significance level of 1%, what is the area to the right of the critical value?

  α/2
• What does it mean in hypothesis testing to fail to reject the null hypothesis?

  Insufficient evidence for alternative
• What is a Type I error in hypothesis testing?

  Rejecting H₀ when true