Final answer:
The matching involved a one-sample t-test and a one-sample z-test, both used to compare a single mean to a population mean, but the t-test is used when population SD is unknown and the z-test when it is known. The independent t-test compares means of two independent samples while the dependent t-test is for means of two related samples.
Step-by-step explanation:
The various statistical tests available are designed to measure different aspects of data, depending on the sample populations and the nature of the data being scrutinized.
Below is the matching of each statistical test with its purpose regarding hypothesis testing:
- A. One-sample t-test - A test of a single mean: This is used when you want to compare the mean of a single sample to a known population mean, but when the population standard deviation (SD) is unknown. Instead, the sample SD is used as an estimate.
- B. Independent t-test - A test of two independent means: This test is used when comparing the means of two separate samples (groups) where the samples are independent, meaning the data in one sample does not affect or relate to the data in the second sample.
- C. Dependent t-test (also known as a paired or matched pairs t-test) - A test of matched pairs: This is applied when comparing the means of two samples that are related in some way, such as measurements before and after a treatment on the same subjects.
- D. One-sample z-test - A test of a single mean: This test compares the mean of a sample to a population mean when the population's standard deviation is known. A z-test is appropriate when the population standard deviation is known and the sample size is large.