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hypotheisSimple

# hypotheisSimple - We wish to determine if a coin is fair or...

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Null hypothesis: Coin is fair that is p=0.5 Alt Hypothesis: Coin is not fair: p not equal to 0.5 n 30 p0 50% observedTails 25 alpha 5% expectedTails 15 distanceToMean 10 upperlimit 25 lowerlimit 5 Pr[ <= lowerlimit] 0 Pr[ >= upperlimit] 0 pvalue 0 verdict Reject H0 We wish to determine if a coin is fair or crooked. We throw the coin n times and a number of tails turn up (this is the observed number of tails). Based on this observation we wish to determine with 1- alpha confidence if the coin is crooked. Farid Alizadeh: Do not confuse these with confidence interval end points! Upper limit is the value that is 10 (or whatever the distance of the observed value to the expected values is) above the expected value, lower limit is the value which is 10 below the expected value Farid Alizadeh: These are probabilities of being 10 or more above the expected value, the next one is the probability of being 10 or more below the expected value. Since the number of tails in n trials follows the binomial distribution, we use BINOMDIST to calculate the CDF. Farid Alizadeh: The p-value is the probability of being 10 away from the expected value. If this value is small, that is smaller than alpha, then the null hypothesis must be rejected. Otherwise the null hypothesis cannot be rejected. Farid Alizadeh: The probability that umber of tails is larger than or equal to 20 is the same as 1 minus the probability that the number of tails is smaller than or equal to 19. Make sure you understand why! Farid Alizadeh: Change the number n and the number of success around and see how the verdict will change along with them

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Hypothesis testing with Z statistic Statistics and other information n 50 mu0 560 sigma 100 alpha 5% sampleMean 580 zValue 1.41 Method 1: P-Value 0.16 pValue 0.16 k Decision: Do not Reject H0 Method 2: Critical region zCritical 1.96 Decision: Do not Reject H0 Method 3: Confidence interval Halfwidth 27.72 lower 552.28 upper 607.72 Decision: Do not Reject H0 Problem: The ETS who put out the SAT tests claims that studying old tests does not have any effect on pe the average SAT scores are 560 with standard deviation of 100. To test ETS's claim we choose a random s and give them two old tests to study. We then collect their scores. Question: At 5% significance level, is there evidence that studying has any effect, positive or negative on S Null hypothesis (H0): The true mean of those who studied past tests is 560 Alternative hypothesis (Ha): The true mean of those who studied the past tests is different (not equal to) To make the decision we must compare the p-value to the critical value which is alpha. If p-value is less tha otherwise it is not rejected. Note that the outcome of the decision should be identical to the critical region m In critical value method we reject the null hypothesis if the zValue falls in the critical region. The critical regio where the acceptance region does not cover. For the two-tailed test the acceptance region is exactly the 1- interval.

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