Test of hypothesis: Testing $H_0: \mu = 28000$ vs $H_a: \mu < 28000,$ based on $n = 40$
observations with $\bar X = 27463$ and $S = 1348,$ we Reject $H_0$
at level 1% because the P-value is less than 1%.
Here are results from Minitab statistical software.
One-Sample T
Test of μ = 28000 vs < 28000
N Mean StDev SE Mean 99% Upper Bound T P
40 27463 1348 213 27980 -2.52 0.008
Obviously, 27463 < 28000. The question is whether it is enough smaller
that we shouldn't ascribe the difference to random variation. The
answer (from the one-sided 99& CI) is that any sample mean below 27980 would
be significantly smaller.
Power computation for specified alternative. Minitab's 'power and sample size' procedure uses the noncentral t
distribution to find power given $n,$ the direction of the test,
the difference between null and alternative values, the significance level, and (an estimate
$\hat \sigma = 1348$ of) of $\sigma.$ The Type II Error probability is 1 - Power, so the probability of Type II error is about 0.123.
1-Sample t Test
Testing mean = null (versus < null)
Calculating power for mean = null + difference
α = 0.01 Assumed standard deviation = 1348
Sample
Difference Size Power
-770 40 0.876884
Power computations require a population variance, or at least the speculation of one. Usual practice is to use
a sample variance as an estimate if one is available. If the true
mean endurance of a tire is as low as 27,230, using data from 40 tires
gives us a pretty good (approx. 88%) chance of detecting that the claimed
28,000 is an exaggeration. (Notice that the difference between $\mu_0$
and this $\mu_1$ is more than a couple of standard errors.)

Notes: (1) Depending on the level of your class, the intention of the exercise may have been to treat this as a power
computation for a z test because $n > 30.$ However, the 'rule' that
t and z tests are 'essentially the same' for $n > 30$ is based on
the fact that the critical value for a one-sided test at the 5% level $t^*$ is close to $z* = 1.645.$ However, for a test at the 1% level
the critical value $t_{.01,39} \approx 2.43$ may not be sufficiently
close to the critical value $z_{.01} \approx 2.33.$
(2) In order to do an accurate power computation for a t test, it is necessary
to use the noncentral t distribution, as in Minitab. Many mathematical
statistics texts have explanations of the noncentral t distribution and
its use in power computations. I found the Wikipedia article to be
unnecessarily technical, but Section 5 of this paper by Scholz may be helpful.