9.6 #12 - Hypothesis Testing for Means

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What is hypothesis testing?

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Hypothesis testing is a statistical method used to make decisions about the value of a population parameter based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (Ha), then using sample data to determine whether to reject H0.

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What is a null hypothesis (H0)?

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The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing.

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What is an alternative hypothesis (Ha)?

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The alternative hypothesis (Ha) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

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When should a z-test be used?

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A z-test should be used when the population standard deviation is known and the sample size is large (typically n > 30).

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When should a t-test be used?

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A t-test should be used when the population standard deviation is unknown and/or the sample size is small (typically n ≤ 30).

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What is the significance level (α) in hypothesis testing?

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The significance level (α) is the probability of rejecting the null hypothesis when it is actually true. Common values are 0.05, 0.01, and 0.10.

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What does a p-value represent in hypothesis testing?

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A p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the assumption that the null hypothesis is true.

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What does it mean to reject the null hypothesis?

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Rejecting the null hypothesis means that there is sufficient evidence to support the alternative hypothesis.

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What does it mean to fail to reject the null hypothesis?

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Failing to reject the null hypothesis means that there is not enough evidence to support the alternative hypothesis.

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What is a one-tailed test?

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A one-tailed test is a hypothesis test that evaluates the direction of the effect, testing whether a parameter is greater than or less than a certain value.