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##### Explain why using the t statistic may be an appropriate alternative to using a z-score (us

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Explain why using the t statistic may be an appropriate alternative to using a z-score (use the concept of estimated standard error to justify your answer).
Oct 13th, 2013

At the point when testing a theory concerning the estimation of a populace mean, either a t-test or a z-test could be conducted. A t-test is a theory test that uses a t-fact, which takes after a t-dissemination. A z-test is a theory that uses a z-fact, which takes after a z-dissemination (a standard typical distribution).

The test should be used if the population variance is unknown and either of the following conditions holds:

• The sample size is large (in general, n ≥ 30); or
• The sample size is small (n ≤ 30), but the population is normally distributed or approximately normally distributed.

The z-test should be used if the population variance is normally distributed with known variance.

For a z-test concerning a single population mean (μ), the test statistic to be used is the z-statistic with n degrees of freedom.

Jul 19th, 2014

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Oct 13th, 2013
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Oct 13th, 2013
Dec 2nd, 2016
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