2.5.1 Introduction to hypothesis testing

• What is hypothesis testing used for?

  To test a claim
• The null hypothesis assumes there is no effect or difference
• The alternative hypothesis suggests there is an effect or difference.
• What is the significance level in hypothesis testing?

  Probability of incorrect rejection
• The test statistic is calculated from sample data
• Steps in the hypothesis testing process

  1️⃣ State the null hypothesis

  2️⃣ State the alternative hypothesis

  3️⃣ Define the significance level

  4️⃣ Calculate the test statistic

  5️⃣ Determine the p-value

  6️⃣ Compare the p-value with the significance level

  7️⃣ Make a decision based on the comparison
• Interpreting the results is the final step in hypothesis testing.
• What does hypothesis testing aim to determine?

  Evidence for a claim
• The null hypothesis assumes there is no effect or difference.
• Match the hypothesis with its description:

  Null Hypothesis ($H_{0}$) ↔️ Assumes no effect or difference

  Alternative Hypothesis ($H_{1}$) ↔️ Suggests there is an effect or difference
• What are common values for the significance level?

  0.05 or 0.01
• A significance level of 0.05 means there is a 5% chance of incorrectly rejecting the null hypothesis.
• What would be the null hypothesis when testing if a new drug reduces blood pressure?

  The drug has no effect
• The null hypothesis is a statement that there is no effect or no difference
• What is the null hypothesis when testing if a coin is fair?

  H_{0}: p = 0.5</latex>
• The significance level is the threshold for rejecting the null hypothesis.
• Match the hypothesis with its example:

  Null Hypothesis ($H_{0}$) ↔️ Mean height of adults is 175 cm: $μ =$$175$

  Alternative Hypothesis ($H_{1}$) ↔️ Mean height of adults is not 175 cm: $μ ≠ 175$
• What is the null hypothesis when testing if a coin is fair?

  H_{0}: p = 0.5</latex>
• The alternative hypothesis suggests there is an effect or difference
• What is the alternative hypothesis when testing if a new fertilizer increases plant growth?

  $H_{1}: μ > μ_{0}$
• If the p-value is less than the significance level, we reject the null hypothesis.
• What does a significance level of 0.05 indicate in hypothesis testing?

  5% incorrect rejection risk
• The significance level is the probability of rejecting the null hypothesis when it is actually true
• The significance level ($α$) is the probability of rejecting the null hypothesis when it is actually true
• In hypothesis testing, if the p-value is less than or equal to α, we reject H₀
• If α = 0.05</latex>, there is a 5% risk of incorrectly rejecting $H_{0}$, which is also known as a Type I error
• Match the significance level with its incorrect rejection probability:

  0.05 ↔️ 5%

  0.01 ↔️ 1%

  0.10 ↔️ 10%
• The test statistic is a value calculated from sample data to assess evidence against the null hypothesis
• The z-statistic is used when the population variance is known or the sample size is large.
• What is the formula for the z-statistic?

  $z =$$\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$
• The t-statistic is used when the population variance is unknown and the sample size is small
• What is the formula for the t-statistic?

  t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}</latex>
• The chi-squared statistic is used for categorical data to test independence or goodness of fit.
• What is the formula for the chi-squared statistic?

  $χ^{2} =$$\sum \frac{(O - E)^{2}}{E}$
• The F-statistic is used for comparing variances between groups in ANOVA
• What is the formula for the F-statistic?

  $F =$$\frac{MSB}{MSW}$
• Match the test statistic with its use case:

  z-statistic ↔️ Large sample or known population variance

  t-statistic ↔️ Small sample and unknown population variance

  Chi-squared statistic ↔️ Categorical data

  F-statistic ↔️ Comparing variances between groups
• Hypothesis testing involves comparing a null hypothesis, which assumes no effect, with an alternative hypothesis, which suggests an effect
• To test if a coin is fair, the null hypothesis is $H_{0}: p =$$0.5$.
• The null hypothesis ($H_{0}$) is a statement that there is no effect or no difference