Question

It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of = 212.9 meters. What is the P-value? a. 0.012 b. 0.050 c. 0.025 d. 0.006 e. Not within ± 0.002 of any of the above

          It is known that driving can be difficult in regions where
winter conditions involve snow-covered roads. For cars equipped
with all-season tires traveling at 90 kilometers per hour, the mean
stopping time in fresh snow is known to be 215 meters, with a
standard deviation of 
 = 2.5 meters. It is often advocated that automobiles in such
areas should be equipped with special tires to compensate for such
conditions, especially with respect to stopping distance. A
manufacturer of tires made for driving in fresh snow claims that
vehicles equipped with their tires have a decreased stopping
distance. A study was done using a random sample of nine snow tires
from the manufacturer on a snow-covered test track. The tests
resulted in a mean stopping distance of 
 = 212.9 meters. What is the P-value?
a.
0.012
b.
0.050
c.
0.025
d.
0.006
e.
Not within ± 0.002 of any of the above

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Added by Elizabeth B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shareef Jackson

12/28/2021

Step 1

9 meters Population mean = 215 meters Population standard deviation = 2.5 meters Sample size = 9 Z = (212.9 - 215) / (2.5 / sqrt(9)) Z = -2.52 Show more…

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It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of = 212.9 meters. What is the P-value? a. 0.012 b. 0.050 c. 0.025 d. 0.006 e. Not within ± 0.002 of any of the above

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Transcript

00:01 Let's say that we know that the average stop time for a car is 215 meters with the standard deviation of 2 .5 meters.

00:10 Now, there's a researcher that's claiming that the average should be lower than 215.

00:15 They take a sample of nine cars and they get an average of 220, sorry, of 12 .9 meters.

00:22 And they want you to find the p value associated with this situation.

00:30 Now, anytime you see words like claim and lower or like higher, that means that they're asking to perform a hypothesis test.

00:42 And a hypothesis test always has a null hypothesis and an alternative hypothesis.

00:49 The null hypothesis is things as they are known, right? and the alternative is what the researcher is trying to prove, right? so we basically know here that the researcher is trying to prove that our average is lower.

01:07 I suggest to always start with the alternate.

01:09 So the researcher is saying that that population mean of 215, that the actual mean is lower than that, right? and the null is like what it's known to be.

01:26 Is known to be equal to 215.

01:29 Right? so these are the like two things that we're basing our hypothesis test on.

01:37 Now, since we know the population mean and the population standard deviation, that means that like that we want to like calculate a z score.

01:51 And z is going to be equal to our sample mean minus our population mean.

02:00 Over our standard error, right, which is our population standard deviation over the square root of the sample size...

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