When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown: Group of answer choices the resulting margin of error for a confidence interval estimate will tend to be fairly small. the t-distribution must be used to obtain the critical value. there will be a large amount of sampling error. None of the above

The t-distribution is used for a normally distributed population when the sample size is small (less than 30) and the population standard deviation is unknown.

Critical value refers to the value that cuts off the highest percentage of the distribution. The critical region is a set of values of the test statistic for which the null hypothesis is rejected in a hypotheses test.

In statistics, if the population standard deviation is known then the z-test is used to test the mean, but if the population standard deviation is not known then the t-test is used.

Assumptions:

The sample size is smaller.

The population is approximately normal.

The population variance is unknown.

The selected samples are a simple random sample.

Based on the information given in the question, small samples are used and the population standard deviation is unknown. The margin of error and sampling error is independent of the small samples and the population standard deviation is unknown.

Hence, the options 1 and 3 are incorrect.

Since small samples are used and the population standard deviation is unknown, the t-distribution must be used to obtain the critical value.

Thus, option 2 is the correct answer.