It is known that driving can be difficult in regions where winter conditions inv

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. Using the sample results and assuming that stopping distance is a Normally distributed random variable, what is the value of the test statistic?

Explanation / Answer

Given that,
population mean(u)=215
standard deviation, =2.5
sample mean, x =212.9
number (n)=9
null, Ho: =215
alternate, H1: !+215
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 212.9-215/(2.5/sqrt(9)
zo = -2.52

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