STAT 5.6 difference of 2 proportions

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What is the difference of two proportions?

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The difference of two proportions refers to the comparison of the proportions of a certain characteristic in two different groups, often represented as PA - PB, where PA is the proportion in group A and PB is the proportion in group B.

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What does P(PA−PB>0) represent?

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P(PA−PB>0) represents the probability that the proportion of a characteristic in group A is greater than that in group B.

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What is a sampling distribution?

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A sampling distribution is the probability distribution of a statistic (like a sample proportion) obtained from a large number of samples drawn from a specific population.

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What is the Central Limit Theorem?

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The Central Limit Theorem states that the sampling distribution of the sample mean (or proportion) will be approximately normally distributed if the sample size is sufficiently large, regardless of the population's distribution.

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What is the formula for the standard deviation of the difference of two proportions?

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The standard deviation of the difference of two proportions is calculated using the formula: sqrt[(pA(1-pA)/nA) + (pB(1-pB)/nB)], where pA and pB are the sample proportions and nA and nB are the sample sizes.

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What is a null hypothesis in the context of comparing two proportions?

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The null hypothesis states that there is no difference between the two population proportions, often expressed as H0: PA = PB.

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What is an alternative hypothesis?

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The alternative hypothesis is the statement that there is a difference between the two population proportions, often expressed as H1: PA ≠ PB.

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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.

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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.

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What is the significance level (alpha) 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.