Identifying Appropriate Test Statistics Involving Population Mean
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- When the variances are known and the sample size is large, a z-test is used to assess whether two population means are different.
- The z-test is best utilized for samples with more than 30 because, according to the central limit theorem, samples with more than 30 samples are assumed to be approximately regularly distributed.
- When the population variance is unknown, however, the t-test is the proper test statistic to apply.
- A t-test compares the means of two samples using statistics. It is used in hypothesis testing, with a null hypothesis of no difference in group means and an alternate hypothesis of a difference in group means that is not zero.
- When asked about probabilities of the mean, sum or total, and/or percentiles means and sums, the Central Limit Theorem should be utilized.
- The Central Limit Theorem implies that if you collect sufficiently enough random samples from a population with mean and standard deviation with replacement, the distribution of the sample means will be nearly normally distributed.
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