Consider a normal population distribution with the value of sigma known. What is

Question

Consider a normal population distribution with the value of sigma known. What is the confidence level for the interval x plusminus 2.81 sigma/Squareroot n? () What is the confidence level for the interval x plusminus 1.45sigma/Squareroot n? () What value of z_a/2 in the Cl formula below results in a confidence level of 99.7%? (Round your answer to two decimal places.) (x - z_alpha/2 middot sigma/Squareroot n, x + z_alpha/2 middot sigma/Squareroot n) Answer the question posed in part (c) for a confidence level of 75%. (Round your answer to two decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

a)

For z = 2.81, by table,

alpha/2 = 0.0025

Hence,

confidence = 1 - alpha = 0.995 = 99.5% [ANSWER]

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b)

For z = 1.45, by table,

alpha/2 = 0.0735

alpha = 0.147

Hence,

confidence = 1 - alpha = 0.853 = 85.3% [ANSWER]

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c)

As c = 0.997, then

alpha/2 = (1-c)/2 = 0.0015

Hence, by table,

z(alpha/2) = 2.97 [ANSWER]

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d)

As c = 0.75, then

alpha/2 = (1-c)/2 = 0.125

Hence, by table,

z(alpha/2) = 1.15 [ANSWER]

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