Homework100B2 - H Problem 3 Suppose we want to test whether...

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STAT 100B HW 2 Due Friday 5pm MS 8971 Problem 1: Suppose in a population of voters, the proportion of those who support a candidate is p . Suppose we get a random sample of 1000 people, and within this sample, the number of people who support this candidate is 530. (1) Calculate the 95% confidence interval for p . Calculate the margin of error. (2) Interpret the confidence level of 95% (so that your roommate can understand you). Problem 2: Continue from Problem 1. Suppose we want to test the hypotheses: H 0 : p = . 5 versus H 1 : p > . 5. (1) Calculate the p-value. (2) Suppose the level of significance is 5%. Should we reject
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Unformatted text preview: H ? Problem 3: Suppose we want to test whether a die is fair or not. In particular, we suspect that the probability of getting a “six” may be greater than 1/6. We roll the die 1000 times, and the number of “six” we observe is 180. (1) Suppose we fix the probability of type I error to be 2 . 5%. Then what is the decision rule? Should we declare that the die is not fair? (2) If the die is indeed not fair, and the probability of getting a “six” is .2. Calculate the probability of type II error of the decision rule in (1). 1...
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