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 σ = 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 are the appropriate null and alternative hypotheses to test the manufacturer's claim?

Answer 1

The null and alternative hypothesis for this test are

`H_0: \mu\ge 215\\\\H_1: \mu< 215`

Explanation:

If we perform a hypothesis test, we can reject or not reject the null hypothesis.

To conclude that the tires have a decreased stopping distance (μ<215), we should state the null hypothesis
`H_0: \mu\ge 215` and then go on with the analysis to reject it (or not).

If the null hypothesis is rejected, the claim of the manufacturer is rigth.

The alternative hypothesis would be
`H_1: \mu<215`, that would turn rigth if the null hypothesis is rejected.