Jasmine wants to see if indoor cats differ from outdoor cats in time spent scratching posts per day. She records 12 indoor and 12 outdoor cats. She has no prediction about which group will scratch more.

Which assumption is required for this independent samples t-test?

Question

Jasmine wants to see if indoor cats differ from outdoor cats in time spent scratching posts per day. She records 12 indoor and 12 outdoor cats. She has no prediction about which group will scratch more.

Which assumption is required for this independent samples t-test?

BlackTom AI · Accepted Answer

When evaluating the assumptions of an independent samples t-test, several key conditions must be considered. 
Option 1: "The data must be normally distributed and have heterogeneity of variance". Here, the notion of heterogeneity of variance (also called unequal variances) is not the standard assumption for the basic independent t-test; in fact, equal variances are assumed (or at least tested for) unless using a variant that adjusts for unequal variances. Thus this option misstates the variance assumption.
Option 2: "The data must be normally distributed and have homogeneity of variance". This aligns with the classic prerequisites: each group should come from a normally distributed population and the two groups should have equal (homogeneous) variances. These conditions ensure the t-test statistic follows the t-distribution under the null hypothesis and that the standard error is appropriately estimated. This option correctly captures the standard assumptions.
Option 3: "The two groups must have equal means". Equating means is not an assumption; it is precisely what the test evaluates for evidence against the null hypothesis. The means are allowed to differ if there is a genuine effect; assuming equality of means would defeat the purpose of the test.
Option 4: "The two groups must have unequal means". Similarly, requiring unequal means is not a methodological assumption for conducting the t-test. The test is designed to detect whether means are different, not to require that they are different. This option confuses the goal of hypothesis testing with an assumption about the true population parameters.
In summary, the only option that correctly states the standard prerequisites for an independent samples t-test is the one describing normal distribution within groups and equal variances between groups, while the other options misrepresent variance requirements or the purpose of the test.

Jasmine wants to see if indoor cats differ from outdoor cats in time spent scratching posts per day. She records 12 indoor and 12 outdoor cats. She has no prediction about which group will scratch more. Which assumption is required for this independent samples t-test?Single choice

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