For large samples when the population standard deviation or

For large samples, when the population standard deviation or is unknown, as long as we are using large samples (n GE 30), The interval estimation of the population mean mu is: mu = X plusminus Z alpha/2 s/squareroot n Where x = sample mean n = sample size S = population standard deviation 1 - alpha = stipulated confidence interval Z alpha/2 = normal standard score For a 90% confidence interval Z alpha/2 = ? For a 95% confidence interval, Z alpha/2 = ? For a 99% confidence interval, Z alpha/2 = ? For a 97.8% confidence interval, Z alpha/2 = ?

Solution

1.

As

alpha/2 = (1 - confidence level)/2 =    0.05  

Then

z(alpha/2) = critical z for the confidence interval =    1.644853627   [ANSWER]

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2.
As

alpha/2 = (1 - confidence level)/2 =    0.025
Then

z(alpha/2) = critical z for the confidence interval =    1.959963985 [ANSWER]

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3.
As

alpha/2 = (1 - confidence level)/2 =    0.005  

Then

z(alpha/2) = critical z for the confidence interval =    2.575829304   [ANSWER]

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4.

As

alpha/2 = (1 - confidence level)/2 =    0.011

Then

z(alpha/2) = critical z for the confidence interval =    2.290367878 [ANSWER]