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 km/hr, the mean stopping time in loose 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 loose snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of 9 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? [Hint you must first state the alternative hypothesis]. Give answer to four decimal places in the form x.xxxx

Explanation / Answer

here null hypothesis: mean =215

alternate hypothesis:mean<215

std error of mean =std deviaiton/(n)1/2 =2.5/(9)1/2 =0.8333

therefore test stat z =(X-mean)/std error =(212.9-215)/0.8333=-2.52

for above p value =0.0059

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