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Questions and Answers
The null hypothesis is represented by the symbol H1.
The null hypothesis is represented by the symbol H1.
False
The primary goal of hypothesis testing is to demonstrate that a treatment does have an effect.
The primary goal of hypothesis testing is to demonstrate that a treatment does have an effect.
False
A discrepancy between sample data and the hypothesis leads to rejecting the null hypothesis only if it is significant.
A discrepancy between sample data and the hypothesis leads to rejecting the null hypothesis only if it is significant.
True
The alternative hypothesis predicts that there is no relationship for the general population.
The alternative hypothesis predicts that there is no relationship for the general population.
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Sample data is used to evaluate the credibility of the alternative hypothesis.
Sample data is used to evaluate the credibility of the alternative hypothesis.
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A sample mean that is very close to 15.8 is consistent with the null hypothesis.
A sample mean that is very close to 15.8 is consistent with the null hypothesis.
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A Type I error occurs when the null hypothesis is correctly accepted.
A Type I error occurs when the null hypothesis is correctly accepted.
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An alpha level of 0.05 corresponds to a confidence interval of approximately 95%.
An alpha level of 0.05 corresponds to a confidence interval of approximately 95%.
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The critical region is where the null hypothesis is always accepted.
The critical region is where the null hypothesis is always accepted.
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If the data shows a significant disparity from the hypothesis, one can conclude the hypothesis is likely correct.
If the data shows a significant disparity from the hypothesis, one can conclude the hypothesis is likely correct.
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Study Notes
Hypothesis Testing
- A hypothesis test uses sample data to evaluate a claim about a population.
- First, state a hypothesis about the population parameter.
- Next, obtain a random sample from the population.
- Compare the sample data with the prediction from the hypothesis.
- If the sample data is consistent with the prediction, the hypothesis is reasonable.
- If there's a large discrepancy between sample data and prediction, the hypothesis is likely wrong.
- The goal is to determine if the treatment has an effect on the population.
Setting Criteria for Decision
- The researcher uses sample data to evaluate the credibility of the null hypothesis.
- Data either supports or refutes the null hypothesis.
- Big discrepancy between data and hypothesis suggests a flawed hypothesis.
The Alpha Level
- The alpha level (significance level) is the probability of making a Type I error.
- It's the probability of incorrectly rejecting a true null hypothesis.
- Common values include 0.05 (5%), 0.01 (1%), or 0.10 (10%).
- A lower alpha level means a stricter criterion for rejecting the null hypothesis.
- Alpha level of 0.05 represents a 5% risk of a Type I error.
Critical Region
- Critical region is the set of values for a test statistic that leads to rejecting the null hypothesis.
- If the calculated test statistic falls within the critical region, the observed data is significantly extreme under the null hypothesis, leading to rejection.
- For example, an alpha level of 0.05 means 5% of the distribution falls in the critical region.
Type I Error (False Positive)
- Occurs when a researcher rejects a true null hypothesis.
- In a typical research situation, a Type I error means a treatment was concluded to have an effect when it actually doesn't.
- The example of a drug failing to work, though is given as a placebo.
Type II Error (False Negative)
- Occurs when a researcher fails to reject a false null hypothesis.
- A Type II error means a real treatment effect goes undetected.
- The example provided is a psychiatrist failing to recognize an effect.
Hypothesis for Directional Test
- A directional test (one-tailed test) specifies the expected direction of the effect or relationship between variables.
- One-tailed tests focus on a specific direction in a distribution, either positive or negative.
One-Tailed Test
- Used when there is a strong theoretical basis suggesting an effect in a particular direction.
Two-Tailed Test
- Used when any effect (positive or negative) is of interest.
Effect Size
- A numerical value expressing the strength of the relationship between variables or the size of group difference.
- A large effect size indicates practical significance of findings, while a small effect size suggests the finding may have limited real-world application.
- Cohen's d measures effect size. Values are described as small (0.2), medium (0.5), or large (0.8).
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Description
This quiz explores key concepts of hypothesis testing, including the formulation of hypotheses, decision criteria, and the significance level. Understand how sample data is used to evaluate population claims and the implications of Type I errors. Ideal for students studying statistics and research methods.
