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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 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?

Respuesta :

Answer:

The null and alternative hypothesis for this test are

[tex]H_0: \mu\ge 215\\\\H_1: \mu< 215[/tex]

Step-by-step 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 [tex]H_0: \mu\ge 215[/tex] 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 [tex]H_1: \mu<215[/tex], that would turn rigth if the null hypothesis is rejected.

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