Final answer:
A t-test is used to determine if there is a significant difference between the means of two groups, appropriate when the population standard deviation is unknown and the sample size is small or moderate. Option 3.
Step-by-step explanation:
The correct answer to the question is 3) Determines if two means are significantly different from each other. A t-test is a type of inferential statistical analysis used to determine if there is a significant difference between the means of two groups, which may be related in certain features.
It is most commonly used when the test statistic follows a Student's t-distribution under the null hypothesis.
Key Characteristics of a t-test
It compares the means from two separate sets of data (unpaired t-test) or two related sets of data (paired t-test).
It is appropriate to use when the population standard deviation is unknown and the sample size is relatively small.
The assumption of the t-test is that the sample data are roughly normally distributed if the sample is not large.
It can be used with a simple random sample and is adaptable even if the sample size is large when the population distribution is not known to be normal.
When performing a hypothesis test using a t-test, statisticians follow a series of steps involving setting up null and alternative hypotheses, collecting and analyzing sample data, and making conclusions about the population based on the sample data.
So Option 3 is the correct answer.