Question

Find the 90% confidence interval for estimating He based on these paired data and assuming normality. (Give your answers correct to one decimal pla Before 63 41 56 66 43 61 33 After 31 31 33 49 36 Lower Limit Upper Limit You may need to use the appropriate table in Appendix B to answer this question.

Answer 1

Calculate the difference of means by subtracting each respective element from both data sets x01 - XO2 = 63 - 31 = 32 x11 -X12 = 61 - 33 = 28 X21 - X22 = 41 - 31 = 10 X31 - X32 = 56 - 33 = 23 X41 - X42 = 66 - 49 = 17 x51 - x52 = 43 - 36 = 7 We then add our of our differences of mean and divide by the number of items in the data set: d = Ex1;- x2 n d = 32 + 28 + 10 + 23 + 17 + 7 6 d = 117 6 d = 19.5 Calculate the sample variance s? by adding the sum of squared differences from the mean: d = (32 - 19.5)2 = 12.52 = 156.25 d = (28 - 19.5)2 = 8.52 = 72.25 d = (10 - 19.5)2 = -9.52 = 90.25 d = (23 - 19.5)2 = 3.52 = 12.25 d = (17 - 19.5)2 = -2.52 = 6.25 d = (7 - 19.5)2 = -12.52 = 156.25 s2 = Sum of Squared Differences n-1 s2 = 156.25 + 72.25 + 90.25 + 12.25 + 6.25 + 156.25 5 S2 = 493.5 5 S2 = 98.7 Now calculate the sample standard deviation s: savs S = 798.7 S = 9.9347873656158 - tscorea/2 x Sd/vñ < d < + tscorea/2 x Savn First find degrees of freedom: Degrees of Freedom = n - 1 Degrees of Freedom = 6 - 1 Degrees of Freedom = 5

First find degrees of freedom: Degrees of Freedom = n - 1 Degrees of Freedom = 6 - 1 Degrees of Freedom = 5 Calculate a: a = 1 - Confidence% a = 1 -0.9 a = 0.1 Find a spread range: a = (a) a = 12(0.1) a = 0.05 Find t-score for Co.05 using 5 degrees of freedom: tscore0.05 = 2.5706 <--- Value can be found on Excel using =TINV(0.1,5) Calculate high end confidence interval total: High End = d + tscorea x sd/vñ High End = 19.5+ 2.5706 x 9.9347873656158/15 High End = 19.5+ 2.5706 x 9.9347873656158/2.4494897427832 High End = 19.5+ 10.425993608381 High End = 29.926 Calculate low end confidence interval total: Low End = d - tscorea x Savn Low End = 19.5 - 2.5706 x 9.9347873656158/15 Low End = 19.5 - 2.5706 x 9.9347873656158/2.4494897427832 Low End = 19.5 + 10.425993608381 Low End = 9.074 Now we have everything, display our 90% confidence interval: 9.074 < d < 29.926

lower limit is 9.074

upper limit is 29.926

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