10) A manufacturer of a gas additive claims that it improves gas mileage. A random sample of 30 drivers tests this claim by determining their gas mileage for a full tank of gas that contains the additive (X1) and for a full tank of gas that does not contain the additive (X2). The sample mean difference D-Bar equals 2.24 miles (in favor of the additive) and the estimated standard error equals 3.0 miles.(a) Using t- test the null hypothesis at the .05 level of significance(b) Specify the p-value for this result. _____________
If true, it probably has more to do with the fact that the bikes with wider tires are sport bikes which by their nature get ridden harder. In any case, your premise (motorcycles having the width of the tyre very large possess less mileage) is shaky. If you want to test the effect of tires on fuel consumption, you have to eliminate other variables. This has been done, to a degree, on KLR650s, which accommodate a wide range of tire types. Bikes running knobby tires have been observed to use more fuel than bikes of the same model running street tires. Some riders have noticed a difference after a tire change. The notion that wide tires increase fuel consumption has some intuitive appeal, but you are going to have some difficulty even showing that it is so, much less isolate a reason.
Larger, softer tyre on the road, more rolling friction. * If a bike requires a larger tyre, it's generally to control more power or weight. More power or weight, less miles per Litre.
a) Ho:The null hypothesis formulated is that there is NO significant difference between the gas mileage BEFORE and AFTER the gas containing the additive Ho: Mu1 Mu2 Ha: Mu1 Mu2 or Mu2 Mu1 (one tailed test) Test statistic t D-Bar / SE 2.24 / 3.0 0.75 b) online p-value calculator is used Degrees of freedom n-1 30-1 29 p-value 0.2296 (for one tailed test) Since the p-value (0.2296) the alpha value (0.05), the Ho will be retained. In other words there is NO evidence to reject the Ho. It can be inferred that the manufacturer's claim that the gas additive improves gas mileage is valid and acceptable.
I can see two reasons for this. Extra rolling resistance of the oversize tire requires more power from the engine. In general, the more power an engine is making at any given time, the more fuel it must consume to make this power. The other reason I see for this is that the motorcycles that tend to use these tires are very high performance bikes. Close to street legal racing bikes. The engines generally make more power and generally operate at a higher RPM than a more tame street bike. High power, high RPM engines will consume more fuel.
