Textbook Question
Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.
c = 0.98, n = 26
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9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
1:38 minutesProblem 7.1.1
Textbook Question
What are the two types of hypotheses used in a hypothesis test? How are they related?
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The two types of hypotheses used in a hypothesis test are the null hypothesis (denoted as H₀) and the alternative hypothesis (denoted as Hₐ).
The null hypothesis (H₀) represents the default or status quo assumption. It is a statement that there is no effect, no difference, or no relationship between variables. For example, H₀ might state that the mean of a population is equal to a specific value.
The alternative hypothesis (Hₐ) is the statement that contradicts the null hypothesis. It represents the claim or effect that the researcher is trying to support. For example, Hₐ might state that the mean of a population is not equal to a specific value, or it could specify a direction (greater than or less than).
The null and alternative hypotheses are mutually exclusive and collectively exhaustive. This means that only one of them can be true, and together they cover all possible outcomes of the test.
The goal of hypothesis testing is to use sample data to determine whether there is enough evidence to reject the null hypothesis (H₀) in favor of the alternative hypothesis (Hₐ), based on a chosen significance level (α).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis (H0)
The null hypothesis is a statement that there is no effect or no difference, serving as a default position in hypothesis testing. It posits that any observed effect in the data is due to sampling variability rather than a true effect. For example, in a drug efficacy test, the null hypothesis might state that the drug has no effect on patients compared to a placebo.
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Step 1: Write Hypotheses
Alternative Hypothesis (H1)
The alternative hypothesis is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. It represents the researcher's claim or what they aim to prove through the hypothesis test. For instance, in the same drug efficacy test, the alternative hypothesis would assert that the drug does have a significant effect on patients.
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Relationship Between Hypotheses
The null and alternative hypotheses are mutually exclusive; if one is true, the other must be false. In hypothesis testing, the goal is to gather evidence to either reject the null hypothesis in favor of the alternative or fail to reject the null. This relationship is fundamental to statistical inference, guiding the decision-making process based on sample data.
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