11.2.3 Inferential Statistics

• What is the primary purpose of inferential statistics?

  Draw conclusions about a population
• Inferential statistics, unlike descriptive statistics, aims to generalize findings from a sample to the entire population.
• The p-value in inferential statistics indicates the likelihood that the observed results occurred by chance
• What p-value is typically used to determine statistical significance?

  $p < 0.05$
• The Null Hypothesis states that there is no significant difference or relationship between variables
• The Alternative Hypothesis claims there is a significant effect or relationship between variables in a population.
• What is the symbol for the Null Hypothesis?

  $H_{0}$
• Match the example with the correct hypothesis type:

  "There is no difference in test scores between two groups." ↔️ Null Hypothesis

  "There is a significant difference in test scores between two groups." ↔️ Alternative Hypothesis
• Statistical significance is measured using the p-value
• What does a p-value of 0.03 indicate in statistical terms?

  Statistically significant result
• A p-value less than 0.05 suggests there is less than a 5% chance the results occurred by chance.
• The Null Hypothesis states there is no significant difference or relationship between variables in a population
• What type of hypothesis claims there is a significant effect between variables?

  Alternative Hypothesis
• What are the two main types of hypotheses used in inferential statistics?

  Null and Alternative
• The null hypothesis states there is no significant difference or relationship between variables
• The alternative hypothesis claims there is a significant effect.
• Match the hypothesis feature with its description:

  Symbol ↔️ $H_{0}$ or $H_{1}$

  Direction ↔️ Directional or Non-directional

  Example ↔️ "There is no difference..."
• What does the p-value represent in hypothesis testing?

  Probability of results
• A p-value of 0.03 is statistically significant because it is less than 0.05
• Understanding statistical significance is essential for generalizing findings to a larger population.
• Which statistical test compares the means of two groups?

  T-test
• ANOVA compares the means of three or more groups
• The chi-square test is used to examine the association between categorical variables.
• Match the statistical test with its example:

  T-test ↔️ "Is there a significant difference in the average heights of men and women?"

  ANOVA ↔️ "Are there significant differences in plant growth among different fertilizer types?"

  Chi-square ↔️ "Is there an association between gender and voting preference?"
• What is the primary purpose of inferential statistics in healthcare?

  Evaluate treatment effectiveness
• In finance, inferential statistics is used to analyze investment portfolios
• A p-value less than 0.05 is considered statistically significant in inferential statistics.
• How does inferential statistics differ from descriptive statistics?

  Makes inferences about populations
• Which statistical test compares the means of two groups?

  T-test
• ANOVA compares the means of three or more groups
• The chi-square test is used to examine the association between categorical variables.
• Match the statistical test with its purpose:

  T-test ↔️ Compare means of two groups

  ANOVA ↔️ Compare means of three or more groups

  Chi-square ↔️ Test association between categorical variables
• In market research, what does inferential statistics help companies understand?

  Customer preferences
• In healthcare, inferential statistics is used to evaluate treatment effectiveness
• Inferential statistics can enhance teaching strategies and improve student outcomes in education.
• What is a potential bias in inferential statistics that can affect the accuracy of results?

  Sample bias
• Small sample sizes reduce statistical power
• Violations of assumptions underlying statistical tests can compromise the accuracy of results.