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in a problem where t-test should be used, what is its degree of freedom if the sample size is 11?
in a problem where t-test should be used, what is its degree of freedom if the sample size is 11?
ANSWER
There is no minimum sample size for the t test to be valid other than it be large enough to calculate the test statistic. Validity requires that the assumptions for the test statistic hold approximately. Those assumptions are in the one sample case that the data are iid normal (or approximately normal) with mean 0 under the null hypothesis and a variance that is unknown but estimated from the sample. In the two sample case it is that both samples are independent of each other and each sample consists of iid normal variables with the two samples having the same mean and a common unknown variance under the null hypothesis. A pooled estimate of variance is used for the statistic.
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