Two Population Means with Unknown Standard Deviations · Try It 1

Two samples are shown in. Both have normal distributions. The means for the two populations are thought to be the same. Is there a difference in the means? Test at the 5% level of significance.

$$\begin{array}{cccc}& \text{Sample Size}& \text{Sample Mean}& \text{Sample Standard Deviation}\\ \text{Population A}& \text{25}& \text{5}& \text{1}\\ \text{Population B}& \text{16}& \text{4.7}& \text{1.2}\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §10.1 Two Population Means with Unknown Standard Deviations · Try It 1