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Example #2: Find $z_{\frac{\alpha}{2}}$ for the confidence level 90%. Example #3: Find $z_{\frac{\alpha}{2}}$ for the confidence level 99%. A confidence interval is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate. Formula for the Confidence Interval of the Mean for a Specific $\alpha$ When $\sigma$ is Known $\bar{X} - z_{\frac{\alpha}{2}} \cdot \left(\frac{\sigma}{\sqrt{n}}\right) < \mu < \bar{X} + z_{\frac{\alpha}{2}} \cdot \left(\frac{\sigma}{\sqrt{n}}\right)$ Confidence Level $z_{\frac{\alpha}{2}}$ 90% 1.65 95% 1.96 99% 2.58 The term $z_{\frac{\alpha}{2}} \left(\frac{\sigma}{\sqrt{n}}\right)$ is called the margin of error E (also called the maximum error of the estimate). It is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter. Assumptions for Finding a Confidence Interval for a Mean When $\sigma$ is Known 1. The sample is a random sample. 2. Either n?30 or the population is normally distributed if n < 30.

          Example #2:
Find $z_{\frac{\alpha}{2}}$ for the confidence level 90%.
Example #3:
Find $z_{\frac{\alpha}{2}}$ for the confidence level 99%.
A confidence interval is a specific interval estimate of a parameter determined by using
data obtained from a sample and by using the specific confidence level of the estimate.
Formula for the Confidence Interval of the Mean for a Specific $\alpha$ When
$\sigma$ is Known
$\bar{X} - z_{\frac{\alpha}{2}} \cdot \left(\frac{\sigma}{\sqrt{n}}\right) < \mu < \bar{X} + z_{\frac{\alpha}{2}} \cdot \left(\frac{\sigma}{\sqrt{n}}\right)$
Confidence Level	$z_{\frac{\alpha}{2}}$
90%	1.65
95%	1.96
99%	2.58
The term $z_{\frac{\alpha}{2}} \left(\frac{\sigma}{\sqrt{n}}\right)$ is called the margin of error E (also called the maximum error of
the estimate). It is the maximum likely difference between the point estimate of a
parameter and the actual value of the parameter.
Assumptions for Finding a Confidence Interval for a Mean
When $\sigma$ is Known
1. The sample is a random sample.
2. Either n?30 or the population is normally distributed if n < 30.

Example #2:
Find z(α)/(2) for the confidence level 90%.
Example #3:
Find z(α)/(2) for the confidence level 99%.
A confidence interval is a specific interval estimate of a parameter determined by using
data obtained from a sample and by using the specific confidence level of the estimate.
Formula for the Confidence Interval of the Mean for a Specific α When
σ is Known
X̅ - z(α)/(2)·((σ)/(√(n))) < μ < X̅ + z(α)/(2)·((σ)/(√(n)))
Confidence Level z(α)/(2)
90% 1.65
95% 1.96
99% 2.58
The term z(α)/(2)((σ)/(√(n))) is called the margin of error E (also called the maximum error of
the estimate). It is the maximum likely difference between the point estimate of a
parameter and the actual value of the parameter.
Assumptions for Finding a Confidence Interval for a Mean
When σ is Known
1. The sample is a random sample.
2. Either n?30 or the population is normally distributed if n < 30.

Added by Javier B.

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