Large-Sample Test of a2 = s02: When n > 30 we can test the null hypothesis that s = a02, or s — (To, by computing which is a value of a random variable whose sampling distribution is approximately the...

Large-Sample Test of a2 = s02: When n > 30 we can test the null hypothesis that s = a02, or s — (To, by computing which is a value of a random variable whose sampling distribution is approximately the standard normal distribution.

(a) With reference to Example 10.5, test, at, the 0.05 level of significance whether s = 10.0 years against the alternative that s ? 10.0 years.

(b) It is suspected that, the variance of the distribution of distances in kilometers achieved per 5 liters of fuel by a new automobile model equipped with a diesel engine is less than the variance of the distribution of distances achieved by the same model equipped with a six-cylinder gasoline engine, which is known to be s2 = 6.25. If 72 test runs in the diesel model have a variance of 4.41, can we conclude at the 0.05 level of significance that the variance of the distances achieved by the: diesel model is less than that of the gasoline model?