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Question 3 (4 marks) Part a) Given the following information X-500, σ=12, n=50 i) Determine the 95% confidence interval estimate of population mean. ii) Determine the 99% o confidence interval estimate of population mean Part b) A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are X-120 and s-15. (i) Estimate the population mean with 95% confidence level (ii) Estimate the population mean with 99% confidence level.

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D Civen, wle hawe to find s confidence inten estimate of wir have conidence lo c 357 Hence, 0.05 Using enhcal Vaule ttble for standa 여 nomnaj alism buton 1 2 E3 326 2 rcfere, 957 confitence intenval is (4366738, 303-3162) i) No co , ug ehave to行nd eeggy, confidence interval 1196.6738, 5o3.316 Hence, oe= 0.01 using cri hca1 Valu etable, Zeニ2.575 (435.6 30,SD4.36) Therefore, gg % confidence interval isfat b) erau e to fintあ35% confidente interno) estimate of populoion mean Here, degrees of freedomニS-leSo Usiny table of citical values for t-distibuhion te =2009 IS E = 4.2157 Therefore, gry, confidence intenued is (!is. 7803/ 124.2137) Nou) eo e have to fint gg%. confidence interv . nfidince inten is (115-7803, 124.2491 OTS, 93 usin, table of Critica) values , te=2-678 xt E = 120 t 5.624 3ニ125. 62113 is (114-31st, ,25,62Hg) interva/ Therefore, g3% confidence

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