A manufacturer claims its Brand \(A\) battery lasts longer than its competitor's Brand \(B\) battery. Nine batteries of each brand are tested independently, and the hours of battery life are shown in the table below.

$$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline \text{Brand }A & 88 & 85 & 80 & 81 & 72 &90 & 85 & 85 &84 \\ \hline \text{Brand }B & 80 & 79 & 87 & 82 & 75 &81 & 77 & 73 &78 \\ \hline \end{array} $$

Provided that the assumptions for inference are met, which of the following tests should be conducted to determine if Brand \(A\) batteries do, in fact, last longer than Brand \(B\) batteries?

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The sample sizes are not large enough and the standard deviations are unknown, so a \(z\)-test would not be appropriate. We want to do a one-sided test since we want to know if one of the batteries lasts longer than the other (\(A-B \gt 0\)).

A paired \(t\)-test is not appropriate because the batteries were not paired to before and after treatments.