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fin05sol - Suggested solution Question 1(a The Hypothesis...

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1 Suggested solution Question 1: (a) The Hypothesis statement is H 0 : μ <=23 vs H 1 μ >23. Naturally we need to assume that that either the data are normally distributed in which case we can use a t-test or assume that the CLT applies. That is n=56 is large enough and we can use the Z-test. Using the t-test approach the test statistic is T=sqrt(56)(23.5-23)/10.2=.367 There are 55 degrees of freedom and we can use the normal table to find the critical value of 1.645 at alpha =.05. In this case since .367<1.645 we cannot reject the null hypothesis and must conclude that the evidence indicates that their claim is false. (b) The 95% confidence interval is approximately 23.5+-2.67 (c) To find A, solve the equation sqrt(56)(23.5-A)/10.2 >=1.645, the solution is A<=21.258. Hence set A=21. Note: Question (c) can be adjusted for different values of the standard deviation. Question 2: (a) Using the formula for the differences where the population variances are assumed equal but unknown we first find 2K=16.14+6.14 or K=11.14, but K=T .025 SE, With 10 degrees of freedom T .025 =2.228, hence the Standard Error is 5
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