Final answer:
The t-test is not designed to count cases in groups but to compare the means of two groups to see if they differ significantly. The paired sample t-test compares two related samples, while the Aspin-Welch t-test is used for two independent means with unknown and unequal variances. A test for independence involves different degrees of freedom and compares observed and expected frequencies.
Step-by-step explanation:
The statement that the t-test is designed to examine the number of cases in two groups to determine which one has the most cases is false. The t-test is actually a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in the case of a paired sample t-test or independent with the independent sample t-test.
When we perform a hypothesis test using the t-test on matched or paired samples, such as pre-test and post-test scores for the same subject, the key concepts include:
- Two measurements are drawn from the same pair of individuals or objects (this is true).
- Two sample means are compared against each other to see if they differ significantly (this is true).
It's also worth noting that the Aspin-Welch t-test is used when comparing two independent population means where the population standard deviations are unknown and possibly unequal. This test employs a special formula to calculate degrees of freedom.
In a test for independence, such as when looking at whether college choice is related to socioeconomic status, the number of degrees of freedom is typically (number of rows - 1) multiplied by (number of columns - 1), not simply the sample size minus one. At the same time, a test of independence indeed involves comparing observed to expected frequencies to assess any association between categorical variables.
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