Consider a normal population distribution with the value of sigma known. (a) Wha

Question

Consider a normal population distribution with the value of sigma known. (a) What is the confidence level for the interval x^bar plusminus 2.81 sigma/squareroot n? _______ % (b) What is the confidence level for the interval x^bar plusminus 1.46 sigma/squareroot n? (c) what value of z_alpha/2 in the CI formula below results in a confidence level of 99.7%? (x^bar - z_alpha/2 middot sigma/squareroot n, x^bar + z_alpha/2 middot sigma/squareroot n) z_alpha/2 = ________ (d) Answer the question posed in part (c) for a confidence level of 75%. Z_alpha/2 = ________

Explanation / Answer

a)

z-score = 2.81

=>

z(alpha/2) = 2.81

=>

alpha =0.005

hence confidence interval is 99.5%

b)

alpha = 0.08

confidence interval is 92.8%

c)

z(alpha/2) = 3

d)

z(alpha/2) = 1.15

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