Answer:
No, the owners are not having their transmissions serviced at 30,000 miles.
Step-by-step explanation:
We are given that a car dealer recommends that transmissions be serviced at 30,000 miles.
The car dealer selects a random sample of 40 customers and finds that the average mileage of the automobiles serviced is 30,456. The standard deviation of the population is 1684 miles.
Let = <em>true average mileage of the automobiles serviced</em>.
So, Null Hypothesis, : = 30,000 miles {means that the owners are having their transmissions serviced at 30,000 miles}
Alternate Hypothesis, : 30,000 miles {means that the owners are having their transmissions serviced at different than 30,000 miles}
The test statistics that will be used here is <u>One-sample z-test statistics</u> because we know about population standard deviation;
T.S. = ~ N(0,1)
where, = sample average mileage serviced = 30,456 miles
= population standard deviation = 1684 miles
n = sample of customers = 40
So, <u><em>the test statistics</em></u> =
= 1.71
The value of z-statistics is 1.71.
<u>Also, the P-value of the test statistics is given by;</u>
P-value = P(Z > 1.71) = 1 - P(Z 1.71)
= 1 - 0.9564 = 0.0436
For the two-tailed test, the P-value is calculated as = 2 0.0436 = <u>0.0872</u>.
Since the P-value of our test statistics is less than the level of significance as 0.0872 < 0.10, so <u><em>we have sufficient evidence to reject our null hypothesis</em></u> as the test statistics will fall in the rejection region.
Therefore, we conclude that the owners are having their transmissions serviced at different than 30,000 miles.