When conducting inference about the difference between two population means, which of the following assumptions is NOT required?a.Independence of observations within each sampleb.Normality of the populations being comparedc.Equality of population variancesd.Random sampling from the populations
Question
When conducting inference about the difference between two population means, which of the following assumptions is NOT required?a.Independence of observations within each sampleb.Normality of the populations being comparedc.Equality of population variancesd.Random sampling from the populations
Solution
To determine which assumption is NOT required when conducting inference about the difference between two population means, let's analyze each option:
a. Independence of observations within each sample: This assumption is necessary because it ensures that the observations within each sample are not influenced by each other. Therefore, this assumption is required.
b. Normality of the populations being compared: This assumption is also necessary because it allows us to use parametric tests, such as the t-test, which rely on the assumption of normality. Therefore, this assumption is required.
c. Equality of population variances: This assumption is known as the assumption of equal variances. While it is often assumed, it is not always required. There are tests, such as the Welch's t-test, that can be used when the assumption of equal variances is violated. Therefore, this assumption is not always required.
d. Random sampling from the populations: This assumption is necessary because it ensures that the samples are representative of the populations being studied. Therefore, this assumption is required.
Based on the analysis above, the assumption that is NOT required when conducting inference about the difference between two population means is c. Equality of population variances.
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