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Questions and Answers
What is typically used to determine the area of rejection in hypothesis testing?
What is typically used to determine the area of rejection in hypothesis testing?
- Standard deviation of the sample
- Sample size determination
- Confidence interval range
- P-value of the test statistic (correct)
What is the level of significance generally used in hypothesis testing?
What is the level of significance generally used in hypothesis testing?
- 0.1
- 0.25
- 0.05 (correct)
- 0.01
Which statistical tests belong to the T-test family?
Which statistical tests belong to the T-test family?
- Independent samples T-test and Paired samples T-test (correct)
- Chi-square test and Mann-Whitney U test
- One-sample T-test and ANOVA
- Regression analysis and Correlation analysis
Which of the following is NOT a purpose of statistical tests in bioepidemiology?
Which of the following is NOT a purpose of statistical tests in bioepidemiology?
In formulating a hypothesis, which statement is correctly framed?
In formulating a hypothesis, which statement is correctly framed?
What is the significance of defining the Area of Rejection in hypothesis testing?
What is the significance of defining the Area of Rejection in hypothesis testing?
When selecting a level of significance (α) in hypothesis testing, what does it represent?
When selecting a level of significance (α) in hypothesis testing, what does it represent?
Which of the following correctly describes the formulation of the null hypothesis (Ho) and alternative hypothesis (Ha)?
Which of the following correctly describes the formulation of the null hypothesis (Ho) and alternative hypothesis (Ha)?
Which statistic is most appropriate for comparing the means of a sample to a known population mean when the sample size is large?
Which statistic is most appropriate for comparing the means of a sample to a known population mean when the sample size is large?
In the example where a teacher claims the mean score of students in his class is greater than 82, which type of test should be used?
In the example where a teacher claims the mean score of students in his class is greater than 82, which type of test should be used?
What is the correct definition of the Area of Rejection in hypothesis testing?
What is the correct definition of the Area of Rejection in hypothesis testing?
How is the level of significance (α) important in hypothesis testing?
How is the level of significance (α) important in hypothesis testing?
For a paired t-test, what is the formula for the degrees of freedom (df)?
For a paired t-test, what is the formula for the degrees of freedom (df)?
What type of t-test is used when comparing two independent groups?
What type of t-test is used when comparing two independent groups?
In hypothesis formulation, what does the null hypothesis (H0) typically state?
In hypothesis formulation, what does the null hypothesis (H0) typically state?
If the critical value of a two-tailed test at the 1% significance level is ±2.845, what would be the decision if the test statistic is 3.0?
If the critical value of a two-tailed test at the 1% significance level is ±2.845, what would be the decision if the test statistic is 3.0?
What is an incorrect interpretation of a two-tailed significance level of 0.05?
What is an incorrect interpretation of a two-tailed significance level of 0.05?
What is the role of the test statistic in hypothesis testing?
What is the role of the test statistic in hypothesis testing?
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Study Notes
Hypothesis Testing
- Hypothesis testing is a statistical method used to determine whether there is enough evidence to support a claim about a population.
- There are two types of hypotheses:
- Null hypothesis (H0): It states that there is no significant difference between the groups being compared.
- Alternative hypothesis (Ha): It states that there is a significant difference between the groups being compared.
- The level of significance (α) is the probability of rejecting the null hypothesis when it is actually true.
- The area of rejection is the region in the sampling distribution where the test statistic falls, leading to the rejection of the null hypothesis.
- The test statistic is a value that is calculated from the sample data to test the hypothesis.
- The conclusion is based on the comparison of the test statistic to the critical value. If the test statistic falls within the area of rejection, the null hypothesis is rejected.
Example #4
- The teacher claims that the mean score of students in his class is greater than 82.
- The null hypothesis (H0) is that the mean score is not greater than 82.
- The alternative hypothesis (Ha) is that the mean score is greater than 82.
- The level of significance (α) is 0.05.
- The test statistic used is the z-test.
- The critical value for a one-tailed test with α = 0.05 is 1.645.
- The test statistic is calculated to be 3.23.
- Since 3.23 is greater than 1.645, the null hypothesis is rejected.
- The conclusion is that there is enough evidence to support the teacher's claim.
Example #5
- The null hypothesis (H0) is that there is no significant difference between the two groups.
- The alternative hypothesis (Ha) is that there is a significant difference between the two groups.
- The level of significance (α) is 0.01.
- The test statistic used is the unpaired/independent t-test.
- The critical value for a two-tailed test with α = 0.01 is ±2.845.
- The area of rejection is the region in the sampling distribution where the test statistic falls outside the range of -2.845 and +2.845.
Choosing Statistical Tests
- Parametric statistical tests require data to be normally distributed, while non-parametric tests do not.
- The type of statistical test used depends on the type of data and the research question. Choices for parametric tests include:
- Chi-square family
- T-test family
- Correlation family
- Parametric tests are used when the data is continuous and the goal is to compare or analyze relationships between variables.
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