AP Statistics Hypothesis Tests for Means

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What is a one-sample T-test for a population mean?

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A statistical test used to determine if the mean of a single sample is significantly different from a known or hypothesized population mean, especially when the population standard deviation is unknown.

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What is the null hypothesis (H0) in hypothesis testing?

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The null hypothesis is a statement that there is no effect or no difference, and it serves as the default assumption that any observed effect is due to sampling variability.

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What is the alternative hypothesis (Ha)?

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

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What is a Type I error?

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A Type I error occurs when the null hypothesis is rejected when it is actually true, also known as a false positive.

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What is a Type II error?

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A Type II error occurs when the null hypothesis is not rejected when it is actually false, also known as a false negative.

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What does the significance level (alpha) represent in hypothesis testing?

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The significance level (alpha) is the probability of making a Type I error, commonly set at 0.05 or 0.01.

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What is the purpose of a one-sample Z-test?

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A one-sample Z-test is used to determine if the mean of a single sample is significantly different from a known population mean when the population standard deviation is known.

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What is the formula for the test statistic in a one-sample T-test?

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What is the difference between a one-sample T-test and a one-sample Z-test?

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A one-sample T-test is used when the population standard deviation is unknown and the sample size is small, while a one-sample Z-test is used when the population standard deviation is known or the sample size is large.

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What is the purpose of conducting a hypothesis test?

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The purpose of conducting a hypothesis test is to make inferences about a population based on sample data, determining whether to reject or fail to reject the null hypothesis.