Hypothesis tests

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What is a hypothesis test?

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A hypothesis test is a statistical method used to make decisions about the properties of a population 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 p-value?

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A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. It helps determine the strength of the evidence against the null hypothesis.

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What does it mean to reject the null hypothesis?

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Rejecting the null hypothesis means that the sample data provides sufficient evidence to support the alternative hypothesis. This typically occurs when the p-value is less than the significance level (alpha).

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What is the significance level (alpha)?

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The significance level (alpha) is the threshold for determining whether to reject the null hypothesis. Common values are 0.05, 0.01, and 0.10.

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What is a one-sample z-test?

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A one-sample z-test is a statistical test used to determine whether the mean of a single sample is significantly different from a known population mean when the population variance is known.

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What is a one-proportion z-test?

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A one-proportion z-test is used to determine whether the proportion of a single sample is significantly different from a known population proportion.

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What does it mean if the p-value is less than alpha?

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If the p-value is less than alpha, it indicates strong evidence against the null hypothesis, leading to its rejection.

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What does it mean if the p-value is greater than alpha?

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If the p-value is greater than alpha, it indicates insufficient evidence to reject the null hypothesis, leading to a failure to reject it.

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What is the 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 the alternative hypothesis (Ha)?

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The alternative hypothesis (Ha) is a statement that indicates the presence of an effect or a difference, and it is what the researcher aims to support.