Final answer:
The statement is true; the independent groups t test is used for comparing the means of two independent groups when population standard deviations are unknown. For more than two levels, one-way ANOVA is used. For two proportions or known standard deviations, different tests apply.
Step-by-step explanation:
The statement 'The independent groups t test is used for between subjects designs with two and only two levels' is true. The independent samples t test compares the means of two separate groups to determine if there is a statistically significant difference between them. This test is appropriate when working with two independent groups under the condition that the population standard deviations are unknown. It is not suitable for designs with more than two levels; in such cases, a one-way ANOVA is used instead.
When we consider independence in statistics, we often refer to the test of independence that utilizes the chi-square distribution. This test assesses whether two categorical variables are independent of each other. To conduct this test, a contingency table is created to analyze observed and expected frequencies. The null hypothesis states that there is no association between the variables (they are independent). It is not connected to the independent samples t test and has different applicability, such as examining the relationship between a student's college choice and their socioeconomic status.
To compare two proportions, such as the proportion of males and females passing their driver's test on the first attempt, you would use a test of two proportions rather than an independent samples t test.
Finally, when comparing the means of two groups where population standard deviations are known, a different statistical test is used, which takes into account this additional information. For example, comparing the effectiveness of a powder diet versus a liquid diet with known population standard deviations would require a different methodology than an independent samples t test.