I need someone to explain to me why they chose right tail in

I need someone to explain to me why they chose right tail instead of left(keep in mind that the solution might be wrong), I need to understand when to use left and when to use right tail testing and in the context of this question, it might help me understand if explained in detail.

We notice that n = 64, so we can assume by the Central Limit Theorem that sigma S = 33.9, the null hypothesis is true, then the distribution of is approximately standard normal. We notice that Hence, H0 is rejected at alpha = 0.05 (since 2.10 > 1.645). The lifetime of a. certain type of emergency batteries is normally distributed. A sample of 64 batteries has produced a sample mean of 756.4 hours and a sample standard deviation of 33.9 hours. (a) Test the null hypothesis H0 : Mu 747.5 at. the significance level of alpha 1 = 0.05.

Solution

A right tailed test is appropriate here. Because the alternative hypothesis here specifies a region towards right side of the hypthesized value i.e. 747.5. A test is detremined as a left tailed one or a right tailed one based on whether the area it specifies lying below the hypothesized value or lying above it. Here the test specifies an area above the hypothesized value in terms of alternative hypothesis.