Answer:
We accept the alternate hypothesis. We conclude that the mean lifetime of tires is is less than 33,000 miles.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 33,000 miles
Sample mean,
= 32, 450 miles
Sample size, n = 18
Alpha, α = 0.05
Sample standard deviation, s = 1200 miles
a) First, we design the null and the alternate hypothesis
b) Level of significance:
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.05)
c) We use One-tailed t test to perform this hypothesis.
d) Formula:
Putting all the values, we have
Now,
Rejection area:
![t < -1.7396](https://tex.z-dn.net/?f=t%20%3C%20-1.7396)
Since,
e) We fail to accept the null hypothesis and reject it as the calculated value of t lies in the rejection area.
f) We accept the alternate hypothesis. We conclude that the mean lifetime of tires is is less than 33,000 miles.