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COMM 291
Jonathan Berkowitz

Question 1 a) ̅ √ √ 80% 90% 95% 99% b) This is a false explanation of statistical significance. 0.05 is a probability that describes the sample mean ̅ not population mean . c) Yes , this statement is essentially correct. Significant results have low p-values and p-values tell us the probability of making an observation due to chance alone. d) The null hypothesis represents that there is no effect: . The alternative hypothesis represents that there is an effect: . e) i) The Hypothesis always refers to the population parameter not sample statistic. ii) There is no significance level that would allow us to reject the null hypothesis with a p-value this high. iii) A confidence level of 100% would have an infinite range, so this isn’t very useful. iv) No, it is ̂ ̂ (Forgot z) v) No, it is based on the z-statistic. Question 2 ̂̂ a) √ 1. √ 2. √ b) 1. 2. 95% CI 1. 0. 2. c) 1. We are 95% confident that the true proportion of investors that have at least $10,000 invested in the stock market lies between 61.472% and 68.528%. 2. We are 95% confident that the true proportion of investors that are more likely to invest $10,000 in stocks over bonds lies between 44.476% and 51.524%. ̂̂ d) √ 1. √ 2. √ Question 3 a) We are interested in whether the cracking rate of the Ingots has decreased, hence 1-sided. b) ̂ √ 100 Ingots 1000 Ingots ̂ √ ̂ √ ̂ ̂ ̂ ̂ P-value For the sample of 100 Ingots, there is no evidence to conclude that the mean of the population of Ingots from w
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