Assume the competing hypotheses take the following form: versus ,where is the population mean for population 1 and is the population mean for population 2.Also assume that the populations are normally distributed and we use independent sampling.The population variances are not known and cannot be assumed equal.The value of the appropriate test statistic is computed as ____________.

Question

Assume the competing hypotheses take the following form:  versus  ,where  is the population mean for population 1 and  is the population mean for population 2.Also assume that the populations are normally distributed and we use independent sampling.The population variances are not known and cannot be assumed equal.The value of the appropriate test statistic is computed as ____________.

Quizplus · Accepted Answer

This question is asking for the test statistic for a two-sample t-test with unequal variances. The formula for this test statistic is:

t = (x̄_1 - x̄_2) / sqrt[(s_1^2 / n_1) + (s_2^2 / n_2)]

where x̄_1 and x̄_2 are the sample means, s_1 and s_2 are the sample standard deviations, and n_1 and n_2 are the sample sizes for populations 1 and 2, respectively.

Without any information about the sample means, standard deviations, or sizes, we cannot calculate the test statistic directly. However, we do know that the populations are normally distributed and that the variances are not assumed to be equal. This suggests that we should use a two-sample t-test with unequal variances.

The answer choice that corresponds to this test statistic formula is B, 11eaa4ae_7ab7_ec78_9180_ef13c1c42bfc_TB2339_11.

Assume the Competing Hypotheses Take the Following Form: Versus