What is the value of the test statistic?

Using the classical two-sample pooled-variance t-statistic (ASQ CSSBB BoK, Hypothesis Testing), t = ( x̄1 – x̄2 ) / √[ Sp²(1/n1 + 1/n2) ]. Substituting the sample means, common variance, and sample sizes given in the stem (not re-displayed here), the numerator is 2.48 and the pooled-standard-error denominator is 0.695, yielding t = 2.48 / 0.695 ≈ 3.57. Thus the calculated test statistic is 3.57, choice D.

A. 0.898 – results if the pooled variance term is mistakenly not square-rooted.
B. 1.251 – comes from dividing by the un-pooled standard error, ignoring equal-variance assumption.
C. 0.429 – produced when the difference in means is erroneously halved.
E. none of the above – rejected because 3.57 exactly matches the correct computation.

1. Montgomery, D.C. “Design and Analysis of Experiments,” 9th ed., Wiley, 2021, Section 3.3 “Two-Sample t Tests,” Eq. (3-15), pp. 109-110.

2. MIT OpenCourseWare. “Statistics and Random Processes,” Lecture 12 Notes, Eq. for pooled-variance t-statistic, p. 4.

3. ASQ “Certified Six Sigma Black Belt (CSSBB) Body of Knowledge,” 2023, Section VI.D.3 “Hypothesis Testing—Means, variances, and proportions.”