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Use m np and s 1npq confidence intervals using two

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Unformatted text preview: Use m = np and s = 1npq. Confidence Intervals (Using Two Samples) Two Proportions: N N N N 1 p1 - p22 - E 6 1 p1 - p22 6 1 p1 - p22 + E where E = za>2 NN p1q1 NN p2q2 n2 Common Critical z Values CONFIDENCE INTERVAL Confidence Level 0.90 0.95 0.99 Critical Value 1.645 1.96 2.575 Choosing Between z and t for Inferences about Mean • • • s known and normally distributed population: use z s known and n 7 30: use z s unknown and normally distributed population: use t Hypothesis Testing (Two Proportions or Two Independent Means) Two Proportions: Requires two independent simple random samples and np Ú 5 and nq Ú 5 for each. Test statistic: z= N N 1 p1 - p22 - 1 p1 - p22 pq pq n2 Matched Pairs Requires simple random samples of matched pairs and either the number of matched pairs is n 7 30 or the pairs have differences from a population with a distribution that is approximately normal. d: Individual difference between values in a single matched pair md: Population mean difference for all matched pairs d: Mean of all sample differences d sd: Standard deviation of all sample differences d n: Number of pairs of data d - md Test statistic: t = where df = n - 1 sd 1n Probability Rare Event Rule: If, under a given assumption, the probability of an event is extremely small, conclude that the assumption is probably not...
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