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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 usedData is normally distributed

Null and Alternative Hypothesis

Ho: population means is equal to μo. μ = μoHa1: 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 StatisticCritical value

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)

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

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.

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