# Z Test

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- Assumptions

- One sample Z test is used when the sample size is large (> 30) or population standard deviation is known.
- Method of simple random sampling is used
- Data is normally distributed

- 5-Step Hypothesis

## Null and Alternative Hypothesis

- Ho: population means is equal to μo. μ = μo
- Ha1: population means is equal to μo. μ≠μo (Two-tailed test)

Ha2: population means is equal to μo. μ<μo (Left tailed test)

Ha3: population means is equal to μo. μ>μo (Right tailed test)

Here μ_o takes a particular value.

## Test Statistic

## Critical value

- -z(a/2), z(a/2) (Two-tailed test)
- -z(a) (Left tailed test)
- z(a) (Right tailed test)

## P-value

- 2*(1-P(Z≤|z|) (Two-tailed test)
- P(Z≤z) (Left tailed test)
- P(Z≥z) (Right tailed test)

## Decision rule

- Reject Ho if |z|>z(a/2) or p-value < alpha (two-tailed test)
- Reject Ho if –z < -z(a) or p-value < alpha (left tailed test)
- Reject Ho if z > z(a) or p-value < alpha (right-tailed test)

- Confidence Interval

Standard error (SE) and margin of error (ME) is given by:

100(1-alpha)% Confidence interval for the population mean is given by:

This implies I am 100(1-alpha)% confident that estimated population mean lies in the obtained interval.

## One sample z test CALCULATOR

Developed by Versioning Solutions.