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 with known variances and we use independent sampling.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 with known variances and we use independent sampling.The value of the appropriate test statistic is computed as ___________.

Quizplus · Accepted Answer

The appropriate test statistic for independent sample t-test with known variances and normally distributed populations is calculated as:
t = (x̄1 – x̄2) / √ [(s1^2/n1) + (s2^2/n2)]
where,
x̄1 and x̄2 are the sample means
s1^2 and s2^2 are the sample variances
n1 and n2 are the sample sizes.

Here, the sample means are not given, so we cannot calculate the test statistic. Therefore, the answer is not A, B, or D.

Assume the Competing Hypotheses Take the Following Form: Versus