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Questions and Answers
What does the conventional significance level of 0.05 indicate?
What does the conventional significance level of 0.05 indicate?
How does a higher p-value impact the evidence against the null hypothesis?
How does a higher p-value impact the evidence against the null hypothesis?
What is the purpose of setting a strict significance level?
What is the purpose of setting a strict significance level?
When do we reject the null hypothesis based on the p-value?
When do we reject the null hypothesis based on the p-value?
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What does a lower p-value indicate about the evidence against the null hypothesis?
What does a lower p-value indicate about the evidence against the null hypothesis?
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What does the null hypothesis assume?
What does the null hypothesis assume?
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What is the purpose of the alternative hypothesis?
What is the purpose of the alternative hypothesis?
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Which hypothesis determines whether there is enough evidence to reject it in favor of an alternative explanation?
Which hypothesis determines whether there is enough evidence to reject it in favor of an alternative explanation?
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What does the significance level determine in a hypothesis test?
What does the significance level determine in a hypothesis test?
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Which parameter refers to the probability threshold used to evaluate the results of a hypothesis test?
Which parameter refers to the probability threshold used to evaluate the results of a hypothesis test?
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In statistical terms, what does the alternative hypothesis often specify?
In statistical terms, what does the alternative hypothesis often specify?
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Study Notes
One-Sample Hypothesis Testing
Null Hypothesis
The null hypothesis (H₀) is a statement that assumes there is no difference between the observed phenomenon and a hypothetical situation. It represents the traditional viewpoint or the default assumption. In statistical terms, the null hypothesis often states that the population parameter of interest equals a specific value, such as µ = μ₀, where µ denotes the population mean and μ₀ is the hypothesized value. This hypothesis is tested against the alternative hypothesis to determine whether there is enough evidence to reject it in favor of an alternative explanation.
Alternative Hypothesis
The alternative hypothesis (Ha) describes a situation that contradicts the null hypothesis. It represents a new or non-traditional viewpoint and states that there is indeed a difference between the observed phenomenon and the hypothetical situation. In statistical terms, the alternative hypothesis often specifies a different value for the population parameter, such as µ > μ₀ or µ < μ₀, depending on what you are testing. The alternative hypothesis serves as the basis for determining if enough evidence exists to support the rejection of the null hypothesis.
Significance Level
The significance level (α) is the probability threshold used to evaluate the results of a hypothesis test. It determines the likelihood of making a type I error, which occurs when the null hypothesis is rejected even though it is actually true. The conventional significance level is typically set at 0.05, meaning that there is a 5% chance of rejecting the null hypothesis even if it is true. By setting a strict threshold, researchers can minimize the risk of accepting a false positive conclusion.
P-Value
The p-value is the probability of observing a test statistic as extreme as the one computed from the sample data, assuming the null hypothesis is true. It quantifies the strength of the evidence against the null hypothesis. A higher p-value indicates weaker evidence against the null hypothesis, while a lower p-value indicates stronger evidence against the null hypothesis. Typically, if the p-value is less than the chosen significance level, we reject the null hypothesis. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis.
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Description
Learn about the concepts of null and alternative hypotheses in hypothesis testing, including their definitions, roles, and significance in statistical analysis. Explore the significance level and p-value as crucial components in decision-making during hypothesis testing.
