Final answer:
The assumptions of the correlated groups t-test include that the scores in each population have equal variances and the population of difference scores is normally distributed.the correct assumptions for the correlated groups t-test are that the scores in each population have equal variances (a) and the population of difference scores is normally distributed (c).
Step-by-step explanation:
The subject of the question relates to the assumptions made when conducting a correlated groups t-test, a statistical method used to compare the means of two related groups. When discussing the assumptions of the correlated groups t-test, the correct options from the given choices are:
- a) The scores in each population have equal variances.
- c) The population of difference scores is normally distributed.
The assumptions of the correlated groups t-test resemble those of the more commonly known paired sample t-test. Given these options, option b) is incorrect because it references independent samples, which contradicts the correlated nature of this t-test. Option d) is also incorrect because it refers to random assignment to conditions, which is not an assumption of the correlated groups t-test but may apply to experimental designs using independent samples.
To reiterate, the correct assumptions for the correlated groups t-test are that the scores in each population have equal variances (a) and the population of difference scores is normally distributed (c).