What is the confidence level for the interval x plusminus 2.81 sigma/squareroot

Question

What is the confidence level for the interval x plusminus 2.81 sigma/squareroot n? (Round your answer to one decimal place.) What is the confidence level for the interval x plusminus 1.48 sigma/squareroot n? (Round your answer to one decimal place.) What value of z_alpha/2 in the CI 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 78%. (Round your answer to two decimal places.)

Explanation / Answer

a)

As

z(alpha/2) = 2.81

Then by table/technology,

alpha/2 = 0.0025

hence,

alpha = 0.005

So

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

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b)

As

z(alpha/2) = 1.48

Then by table/technology,

alpha/2 = 0.0694

hence,

alpha = 0.1388

So

confidence level = 1 - alpha = 0.8612 = 86.1% [ANSWER]

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c)

Hence,

alpha/2 = (1 - confidence level)/2 =    0.0015

By table/technology,

z(alpha/2) = critical z for the confidence interval =    2.967737925 = 2.97 [ANSWER]

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d)

Hence,

alpha/2 = (1 - confidence level)/2 =    0.11

By table/technology,

z(alpha/2) = critical z for the confidence interval =    1.22652812 = 1.23 [ANSWER]

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