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One-sample hypothesis test - Mr. Olson Video

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Example of how to perform a one-sample statistical hypothesis test.

I explained this in a previous response, but I thought I should explain this again. When performing a hypothesis test for the population mean, and the population standard deviation is unknown (which it almost always is), if you have a random sample and the following conditions apply, you should perform a t-test. (1) The sample size is small compared to the population size (n less than or equal to 0.05N) - this is to account for the fact that in most cases we are sampling from a finite population and we don't have independent trials (and the sampling distribution of the sample mean requires that). (2) The population from which the sample is drawn is normal, OR, the sample size is sufficiently large (which most textbooks say if n is at least 30, although that value is rather conservative in some cases). If neither condition of (2) applies and you have the sample data, you can perform a normal probability plot to determine whether it appears that the data come from a population that is normal, and a modified box-and-whisker plot to make sure there are no outliers (because the test statistic uses the sample mean and the sample standard deviation - both of which are not resistant to outliers). Now, with that being said, because the t-distribution begins to look very similar to the z-distribution when the sample size is greater than or equal to 30, some introductory statistics textbooks encourage the student to just use the z-test when n is greater than or equal to 30 (that's what I did when I wrote this example). However, to be safe, it is best to simply always use the t-test in this situation.๏ปฟ
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