There are several types of Hypothesis Tests here we used a zscore as the test statistic z test All follow the same general steps 1 Define Ho and H1 2 Assume Ho to be true 3 Compute test statistic that will be used to assess the evidence against H0 such as the z score 4 Compute the P value probability assuming Ho to be true of the test statistic showing as great or greater disagreement with that actually observed 5 State a conclusion about the strength of evidence against Ho A method of applying zinc coating to steel is supposed to produce a coating whose mean thickness is no greater than 7 microns A quality inspector measures the thickness of 36 coated specimens and tests H0 7 H1 7 She gets a P value of 0 40 Since P 0 05 she concludes that the mean thickness is within specification Is this conclusion correct The relationship between hypothesis tests and confidence intervals A close one Both are concerned with determining plausible values for parameters such as the mean Hypothesis Test Here we specify particular value or range and determine if it is plausible Confidence Interval Collection of all values of that meet a certain criteria for plausibility x x CI HT A 95 confidence interval for is 1 2 2 0 Based on the data from which the confidence interval was constructed one wants to test H 1 4 0 H 1 1 4 The P value will be a Greater than 0 05 b Less than 0 05 c Equal to 0 05 H o 1 2 For which null hypothesis will P 0 05 H o 1 2 H o 1 2 Tests for a population proportion What is a population proportion No more than 10 of people in Colorado thought that the Colts would beat the Broncos Mean of a bunch of 0 s and 1 s 0 won t beat them 1 will be them The probability of success p 0 10 Is this claim true What are the mean and variance of a Bernoulli trial p 0 10 2 p 1 p From the central limit theorem proportions drawn from the population will have a normal distribution p 0 10 n p 1 p 0 3 n n Ok say we sample 400 fans and get 12 5 thinking that the colts will win H 0 10 How can we test our original claim H1 10 Let s calculate the z value 0 125 0 10 z 1 666 0 3 400 What is the P value 0 0475 What do we conclude Here this is close it is just below 0 05 and may be sufficient to reject the null hypothesis
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