(HW 3.3) Week 3 Homework 3 Problem(1) (a) (2 points) Let Z ~Normal(0, 1). Recall

Question

(HW 3.3) Week 3 Homework 3 Problem(1) (a) (2 points) Let Z ~Normal(0, 1). Recall the definition of z-value, i.e, P(Z > zr) = r. Find the probability of (b) (7 points) Let X1, X2,... , Xn be a random sample from some population with (un- known) mean ? and (known) variance ?2. Based on the Central Limit Theorem and part (a) above, show that the confidence intervals for the population mean u can be estimated by a)22 t b . V?1_ 9s??.DS· 2 ??? 2 (c) (3 points) Find zo/p for each of the following: (i) ? 0.10 (ii) ? = 0.05 (iii)a 0.01

Explanation / Answer

Solutionc:

alpha=0.10

Z alpha/2=1.645

ii)

alpha=0.05

Z alpha/2=1.96

iii)

alpha=1%

Z alpha/2=2.576

confidence level alpha alpha/2 Z alpha/2 90% 10% 5.0% 1.645 95% 5% 2.5% 1.96 98% 2% 1.0% 2.326 99% 1% 0.5% 2.576

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