Large-Sample Test of : When n 30, we can test the null hypothesis that , or = , by computing which is

Large-Sample Test of : When n ≥ 30, we can test the null hypothesis that , or σ = σ , by computing which is a value of a random variable whose sampling distribution is approximately the standard normal distribution.

1. With reference to Example 10.4, test at the 0.05 level of significance whether σ = 10.0 years against the alternative that σ ≠ 10.0 years.

2. It is suspected that the variance of the distribution of distances in kilometers traveled on 5 liters of fuel by a new automobile model equipped with a diesel engine is less than the variance of the distribution of distances traveled by the same model equipped with a six-cylinder gasoline engine, which is known to be σ = 6.25. If 72 test runs of 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 traveled by the diesel model is less than that of the gasoline model?