Thedatasethastheobservations x 1 x 2 x n

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Unformatted text preview: the t‐distribution with (n−1) degrees of freedom such that: 3 P(t ( n − 1) > t c ) = α 2 Chapter 9 Example: Stock market data for 20 successive business days has been collected. The data set has the observations: x 1 , x 2 , . . . , x n daily percentage returns for a company, and y 1 , y 2 , . . . , y n daily percentage returns for a market portfolio. On a given day, stock market prices respond to information about the general economy and therefore, it may be expected that the returns for an individual company may be correlated with the overall performance of the market. That is, a non‐zero covariance between the x and y observations is realistic. The task of interest is to obtain a confidence interval estimate for the difference between the mean return for the company and the mean return for the market portfolio. The differences are generated as: di = xi − yi for i = 1, 2, . . . , 20 The sample mean and standard deviation of the differences were calculated as: d = − 0.173 and sd = 1.391 The negative value for d says that the sample mean for the company returns is less than the sample mean for the market returns. This does not imply that this is the case for the population – the population means are unknown. 4 Chapter 9 For the purpose of the exercise, set the confidenc...
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