Question

What is the z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample? 0. 99 1. 65 1. 96 2. 58.

Answer 1

To specify the accuracy of the mean found for a statistical sample, the amount of error is specified by the margin of error, MOE

• The z-score with a confidence level of 95% is 1.96

Reasons:

The margin of error, MOE, is required when finding a sample mean of a

statistic, which specifies the range within which the true mean is located;

The margin of error is given by the formula;

$\displaystyle MOE = \mathbf{z^* \times \frac{\sigma }{\sqrt{n} }}$

Where:

σ = The standard deviation of the population

n = The sample size

$z^*$ = The z-value based on the applied confidence level.

Using the associated standard normal distribution table, by finding the

area between the z-score and the negative z-score, we have that 95% will

be given by the area between 1.96 and -1.96, which gives, 0.975 - 0.025 = 0.95 = 95%

Therefore;

The z-score at 95% = 1.96

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