Confidence Intervals for the Difference Between 2 Proportions

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What is a confidence interval?

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A confidence interval is a range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter. It is expressed with a certain level of confidence, such as 90% or 95%.

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What does it mean if a confidence interval includes 0?

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If a confidence interval includes 0, it suggests that there is no statistically significant difference between the two proportions being compared.

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

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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 that any observed difference is due to sampling variability.

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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, opposing the null hypothesis.

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What is a test statistic?

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A test statistic is a standardized value that is calculated from sample data during a hypothesis test. It is used to determine whether to reject the null hypothesis.

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What does a p-value represent?

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A 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 (alpha)?

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The significance level (alpha) is the threshold for determining whether a p-value indicates a statistically significant result, commonly set at 0.05 or 0.01.

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What is the formula for the difference between two proportions?

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What does it mean if a test statistic is beyond -2 or +2?

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If a test statistic is beyond -2 or +2, it indicates that the result is more than 2 standard deviations away from the mean, suggesting a small p-value and potential significance.

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What is the interpretation of a 90% confidence interval of (-0.5, 0.7)?

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A 90% confidence interval of (-0.5, 0.7) suggests that we are 90% confident that the true difference in proportions lies within this range, including the possibility of no difference.