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6. (18 points) Suppose that rates of returns on the population of stock market mutual funds follow a normal distribution with expected value fi and variance a. A random sample of 11 stock market mutual funds is drawn. The observed rates of returns are the following! (measured in %): -1.56, 3.40, 1.10, 0.37, 3.79, 1.07, 3.78, 0.89, 4.72, 3.79, 1.11. (i) Report unbiased estimates of u and o?. (ii) What is the sampling distribution of the statistic ? Use the sampling distribution to construct a two-sided level 0.95 confidence interval for . (iii) What is the sampling distribution of (n-1) S? Use the sampling distribution to construct a one-sided level 0.9 upper tail confidence interval CI. =(-0, U.) for the standard deviation o by determining Un

Answer 1

لاگاسلام 2 : 13 = 2ند ما2 - [ط - مكارلا-لا) کی تماید م3%21سال = | ديداها. 52 - ت -يو - و ا2. وو - 2 : 42 10 unbiased estimate of Unbiased estimate of l = sł = 2:18:36 ES – 12.8921 ---- -

ii) sampling distribution of HH ntr - SNG 95%, confidence interval for 4 is obtaineda → Ptky in <taveb-005 may be the * Pftmagen EA <ta-v m) -0.05 + --- -- 4 - मना )= near * pf 5t-tnt, & is cut this is I 95% confidence Interval for l is ft tn 1,00015 set tna, oor sy Here tn 1,0.018 +11,0.05 2.001 1:"95% confidence Interval ford Ps (24836- (2.2014 /2.8go1 2. 1836 +2.2011 2.992 22 = 12:1236_-101285, 21836–1:1285) = 1:0551, 3.3121) The sampling distribution of 101) NXn-

interval, ps obtained as 90% confidence for a consider - plocx <nd) = 0.1 (1-) 0)مد Z= (حلا /o العلاج عن محمد حسام > pl 0² ه وا - 0 goy is confidence interval for عوط ممال - له - ۱x 2.952 بهدهم لا م) حوري2 (5 ،387) هو هو