Hypothesis Testing for proportions

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What is a null hypothesis (H0)?

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A null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as a starting point for statistical testing.

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What is an alternative hypothesis (H1)?

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An 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 is a two-tailed test?

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A two-tailed test is a hypothesis test that checks for the possibility of an effect in two directions, both greater than and less than a certain value.

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What is a one-tailed test?

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A one-tailed test is a hypothesis test that checks for the possibility of an effect in one direction only, either greater than or less than a certain value.

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What does p-value represent in hypothesis testing?

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The p-value represents the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

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

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The significance level (α) is the threshold for rejecting the null hypothesis, commonly set at 0.05 or 5%.

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How do you state the null hypothesis for a proportion?

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The null hypothesis for a proportion is typically stated as H0: p = p0, where p0 is the hypothesized population proportion.

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How do you state the alternative hypothesis for a proportion?

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The alternative hypothesis for a proportion can be stated as H1: p > p0 (greater than), H1: p < p0 (less than), or H1: p ≠ p0 (not equal to).

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What is the formula for calculating the test statistic for proportions?

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The test statistic for proportions is calculated using the formula: z = (p̂ - p0) / sqrt[(p0(1-p0))/n], where p̂ is the sample proportion, p0 is the null hypothesis proportion, and n is the sample size.

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What is a Type I error in hypothesis testing?

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A Type I error occurs when the null hypothesis is rejected when it is actually true.