8.5 practice - hypothesis testing proportions

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What is hypothesis testing?

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Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), 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 (H1)?

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The alternative hypothesis (H1) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

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What does α (alpha) represent in hypothesis testing?

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Alpha (α) represents the significance level in hypothesis testing, which is the probability of rejecting the null hypothesis when it is actually true. Common values are 0.05, 0.01.

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What is a p-value?

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A p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. It helps determine the significance of the results.

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What is a z-test?

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A z-test is a statistical test used to determine whether there is a significant difference between sample and population proportions or means when the population variance is known.

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When should you use a z-test for proportions?

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A z-test for proportions should be used when the sample size is large enough (np and n(1-p) both greater than 5) to ensure the sampling distribution of the proportion is approximately normal.

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What is the formula for calculating the z-score in hypothesis testing for proportions?

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The z-score is calculated using the formula: z = (p̂ - p0) / sqrt[(p0(1-p0)/n)], where p̂ is the sample proportion, p0 is the population proportion, and n is the sample size.

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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 in the sample data 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 in the sample data to support the alternative hypothesis.