Mailing Lists To Purchase
Statistical probability question (the key issue, but simple question)?
An advertiser-mail directly to a recurring problem mailing lists. Historically, approximately 18% of addresses in the list maililing were bad. The advertiser can buy a new list, no right to a small percentage of bad addresses. As a test before buying the new list, the advertiser takes a random sample of 200 addresses and sends catalogs mail. After a certain time arrives, the poster is of the opinion that 32 of the 200 addresses were bad. P (32 less bad addresses) Q = 0.2635), 32 Someonew how bad addresses is certainly lower than the 36 deals in bad expected, based on historical rates of 18%, and recommends to the advertiser buy the new list. How would you react?
I make the following hypothesis test showed that the statistic is not suggesting that the ratio is to test the hypothesis of less than 18% for proportions: Let X be the number of successes in n independent and identically distributed Bernoulli trials, let X ~ binomial (n, p) To test the null hypothesis of the form H0: p = p0, or H0: ≥ or H0: p ≤ p p0 p0 Assuming n * p0> 10 and n * (1-P0)> 10 (some say that the necessary condition here is more high five, I prefer the more conservative assumptions while the approximations in the tail of the distribution are more accurate), then find the test statistic z = (Phat – P0) * / P0 sqrt ((1-P0) / n), where X = Phat / n The p-value test is the area under the normal curve that is consistent with the alternative hypothesis. H1: p ≠ p0, p-value is the area in the tails more | H1 z | p-p value <p0, is the area left of l'A AZ H1: P> p0, p-value is the region the right of z If the p-value less or equal to α level of significance, namely, p-value ≤ α, then reject the null hypothesis and conclude alternative is true. If the value of p above a level of significance, ie the p value> α, then we do not reject the null hypothesis and conclude that the hypothesis null is plausible. Note that we can conclude that the alternative is true, but we can not conclude that the null hypothesis is false, it is plausible. Tests hypothesis to this question is: H0 ≥ p: 0.18 vs. H1: p 0.18 "The test statistic is: z = (0.16 to 0.18) / (√ (0.18 * (1-0.18) / 200) z = -0.7362102 The value of p = P (Z <z) = P (Z <-0.7362102) = 0.2308014 Since the p-value exceeds the significance level of 0.05 does can not reject the null hypothesis and conclude p ≥ 0.18 is plausible.
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