Question

What is the relationship between the Z-Test and confidence interval for Z (Mathematically)?

Answer 1

The formula for the z test and confidence interval are given as below:

Z = (x - μ) / σ

Where,

x - raw score

μ - sample mean

σ - sample standard deviation

Z Score Formula: Standard Error of the Mean:

Z = (x – μ) / (σ / √n)

n - sample size

Confidence interval = x̄  ± Z*Standard error

Confidence interval = x̄  ± Z*M.E

M.E or Standard error - Margin of error

So, mathematically above two formulas are related to each other. The two tailed z test is corresponding to the confidence interval. Note, the confidence interval always provide the results for the two tailed corresponding tests with corresponding level of significance. For example, if the hypothesized population mean is not in the interval, then we can reject the two tailed test.

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