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Questions and Answers
What does a smaller p-value indicate in hypothesis testing?
What does a smaller p-value indicate in hypothesis testing?
- Strong evidence against the null hypothesis (correct)
- Weak evidence against the null hypothesis
- Equal validity of both hypotheses
- Inability to make a decision
What is the purpose of calculating a test statistic?
What is the purpose of calculating a test statistic?
- To compare observed results to the null hypothesis (correct)
- To obtain the p-value
- To summarize the dataset
- To determine the significance level
In hypothesis testing, when do you reject the null hypothesis?
In hypothesis testing, when do you reject the null hypothesis?
- If the p-value is equal to the significance level
- If the p-value is less than the significance level (correct)
- If the test statistic is low
- If the p-value is greater than the significance level
What does the null hypothesis (H0) represent?
What does the null hypothesis (H0) represent?
What is typically the threshold set for rejecting the null hypothesis?
What is typically the threshold set for rejecting the null hypothesis?
What does the alternative hypothesis (Ha) represent?
What does the alternative hypothesis (Ha) represent?
What is the definition of p-value in hypothesis testing?
What is the definition of p-value in hypothesis testing?
What happens if the p-value is greater than the significance level?
What happens if the p-value is greater than the significance level?
Which example best illustrates the null hypothesis?
Which example best illustrates the null hypothesis?
What is an outcome of obtaining a low p-value in a drug effectiveness study?
What is an outcome of obtaining a low p-value in a drug effectiveness study?
What is the primary purpose of hypothesis testing in scientific research?
What is the primary purpose of hypothesis testing in scientific research?
Which statement best defines the null hypothesis (H0)?
Which statement best defines the null hypothesis (H0)?
What does a significance level (α) of 0.05 imply in hypothesis testing?
What does a significance level (α) of 0.05 imply in hypothesis testing?
Which of the following best describes the alternative hypothesis (Ha)?
Which of the following best describes the alternative hypothesis (Ha)?
What is the role of p-value in hypothesis testing?
What is the role of p-value in hypothesis testing?
Which of the following represents a Type I error in hypothesis testing?
Which of the following represents a Type I error in hypothesis testing?
In which step of hypothesis testing is the test statistic calculated?
In which step of hypothesis testing is the test statistic calculated?
What is the final step in the hypothesis testing process?
What is the final step in the hypothesis testing process?
Which of these significance levels is commonly used in hypothesis testing?
Which of these significance levels is commonly used in hypothesis testing?
Which of the following is NOT a step in hypothesis testing?
Which of the following is NOT a step in hypothesis testing?
What does the null hypothesis (H0) state regarding the new drug?
What does the null hypothesis (H0) state regarding the new drug?
What is the alternative hypothesis (Ha) for the new drug?
What is the alternative hypothesis (Ha) for the new drug?
Which statement correctly describes a Type I Error?
Which statement correctly describes a Type I Error?
What does a Type II Error involve?
What does a Type II Error involve?
If researchers reject the null hypothesis, what can they conclude?
If researchers reject the null hypothesis, what can they conclude?
What is a common consequence of a Type I Error in drug testing?
What is a common consequence of a Type I Error in drug testing?
In hypothesis testing, if the null hypothesis is not rejected when it should have been, which error was made?
In hypothesis testing, if the null hypothesis is not rejected when it should have been, which error was made?
Which scenario illustrates the null hypothesis being accepted correctly?
Which scenario illustrates the null hypothesis being accepted correctly?
What is the focus of hypothesis testing in the context of the new drug?
What is the focus of hypothesis testing in the context of the new drug?
When researchers conclude that the new drug is effective when it actually is not, what have they likely committed?
When researchers conclude that the new drug is effective when it actually is not, what have they likely committed?
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Study Notes
Hypothesis Testing
- Hypothesis testing helps determine if there is enough evidence to support a claim about a population.
- Used in research to make inferences and decisions based on sample data.
Why Hypothesis Testing is Important
- Enables data-driven decisions.
- Validates research findings and determines the effectiveness of treatments.
Steps in Hypothesis Testing
- State the Hypotheses:
- Null Hypothesis (H0): No effect or difference. Assumed to be true unless proven otherwise.
- Alternative Hypothesis (Ha): An effect or difference. What you want to prove.
- Choose the Significance Level (α):
- Probability of rejecting the null hypothesis when it is true.
- Common values: 0.05 (5%) or 0.01 (1%).
- Collect and Summarize the Data:
- Gather a sample and calculate relevant statistics (mean, standard deviation, proportion).
- Calculate the Test Statistic:
- A value derived from the data that helps determine whether to reject H0.
- Determine the p-value:
- Probability of obtaining the observed results IF the null hypothesis is true.
- A smaller p-value indicates stronger evidence against H0.
- Make a Decision:
- If p-value ≤ α: Reject H0.
- If p-value > α: Do not reject H0.
Understanding p-value and Significance Level (α)
- p-value: Probability of obtaining the observed result under the assumption of no effect (H0).
- Significance Level (α): Threshold set for rejecting H0, often 0.05.
- Decision Rule:
- Reject H0 if p-value ≤ α.
- Do not reject H0 if p-value > α.
Errors in Hypothesis Testing
- Type I Error (α): Rejecting H0 when it is true (false positive).
- Type II Error (β): Not rejecting H0 when it is false (false negative).
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