# An exercise of interest is to find a 95 confidence

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An exercise of interest is to find a 95% confidence interval estimate for the difference between the population mean closing price in the two sample periods. Stock market prices adjust rapidly to the arrival of new information. Therefore, it is reasonable to consider that the two samples are independent. Summary statistics for the closing prices for the two sample periods are: January to June 124 = x n 89.96 \$ x = 32.54 = 2 x s July to December 128 = y n 97.98 \$ y = 21.45 = 2 y s The pooled variance estimate is: 26.91 = 2 s

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Econ 325 – Chapter 8 11 A confidence interval estimate is calculated as: 128 26.91 124 26.91 97.98 89.96 + ± - c t ) ( A t-distribution critical value c t for a 95% interval estimate is needed. The degrees of freedom is: 250 2 128 124 = - + = - + ) 2 n n ( y x The Appendix Table for the t-distribution does not have an entry for 250 degrees of freedom. However, for 0.025 2 0.05 = = α 2 , 0.025 1.96 1.96 = > > ) Z ( P ) t ( P ) 250 ( where Z is the standard normal random variable. With Microsoft Excel the Function TINV(0.05, 250) returns the answer: 1.969 = c t . Econ 325 – Chapter 8 12 Calculations give a 95% interval estimate for the difference in means for the closing prices in the two sample periods as: [ 6.73 9.31 - - , ] A 99% interval estimate is wider. With 0.01 = α the Microsoft Excel Function TINV(0.01, 250) gives the critical value: 2.596 = c t . For a 99% interval estimate the lower and upper limits are: [ 6.32 9.72 - - , ] The value zero is outside the range of the calculated interval estimate to suggest that the mean closing price is lower in the first sample period compared to the second sample period.
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