One-sample z test

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Z Tests for One Mean: An Example
6:26 — by jbstatistics

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Key Questions

  • The simplest way to explain it is that to do a z test rather than a t test, you need a large enough sample size. For most introductory level classes, that means n is at least 30.

    Fewer than 30 things/people sampled means that you don't have enough data to use the z test.

  • Is it one-population z test? Because we cannot have one sample only in stat experiments. In z test, it is preferable to have n>= 30. We have the formula, z= (computed mean - hypothesized mean) divided by the standard error. SE(standard error) = standard deviation/n.

  • No. You should use student's t-test.

    I'm assuming the population has a normal distribution. The statistic used in the z-test rely on the population standard deviation, so you should use student's t-test, wich depends on the sample standard deviation instead.

    The statistic for student's t-test is #\frac{\barX - \mu_0}{S/\sqrtn# , wich has a t distribution with #n-1# degrees of freedon.

    Also note that since the t-distribution converges to a normal distribution when #n# goes to infinite, if you have a large sample, you can perform t-test similar to the z-test, as the test statistic will have normal distribution.