In a one sample test, a sample is compared with a standard or benchmark. In a two sample test, the samples compared

a. with two alternate hypotheses
b. with an historical and a future benchmark
c. with each other
d. with opposing samples

The correct answer is c. In a two sample test, the samples are compared with each other.

To understand this concept better, let's start by explaining what a hypothesis test is. A hypothesis test is a statistical method used to make inferences or draw conclusions about a population based on sample data. It involves comparing the observed data with a hypothesis or claim about the population.

In a one sample test, you compare the sample data to a standard or benchmark. For example, you might compare the mean weight of a sample of apples to a standard weight specified by the USDA.

On the other hand, in a two sample test, you are comparing two separate samples with each other. This can be done to determine if there is a significant difference between the means of the two samples or if there is an association between two variables. For example, you could compare the average test scores of students who participated in a study program with the average scores of students who did not participate to see if there is a significant difference.

The hypotheses in a two sample test can vary depending on the research question you are trying to answer. Generally, you have two alternate hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis typically assumes that there is no significant difference between the two samples, while the alternative hypothesis suggests that there is a significant difference.

To perform a two sample test, you would calculate a test statistic, such as the t-test for comparing means or the chi-square test for comparing proportions. By comparing the computed test statistic to a critical value from the appropriate distribution (e.g., t-distribution, chi-square distribution), you can determine if there is enough evidence to reject the null hypothesis and support the alternative hypothesis.

So, in summary, a two sample test involves comparing two samples with each other to determine if there is a significant difference between them or to assess the association between two variables. This is done by formulating null and alternative hypotheses and performing a statistical test using an appropriate test statistic.