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We have a random sample of size 17 from the normal distribution N(u,02) where u and o2 are unknown. The sample mean and varia

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(a) For exact confidence interval of a ă t set it is n-1, 1-2/ where th-1, 1-4/2 n is the 1-2/ th MONDO quantile of thoi distwhere Zidh is ot i f ZI 1-dly th the l-4 N/0,1) distribution of x² = (n-1)5² (b) Approximate CI is S Sn. of the quaulile thee) Now s approximally follow N/0², 204 2004) s²-g² N (011), 264 nal ~ N(011), s²-0² 13n-1 =) P P ( 20.025 < 20.975) < (5²_6²Now (£) the confidence interval in part (d) is shifted to left as compared to coufidence interval ine Further confider dence

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