The level of nitrogen oxides (NO_x) in the exhaust of cars of a particular model varies Normally, with standard deviation σ= 0.05 gram per mile (g/mi). Government regulations call for NO_x emissions no higher than 0.3 g/mi. In testing H₀: μ= 0.3 versus H_a: μ

Question

The level of nitrogen oxides (NO_x) in the exhaust of cars of a particular model varies Normally, with standard deviation σ= 0.05 gram per mile (g/mi). Government regulations call for NO_x emissions no higher than 0.3 g/mi. In testing H₀: μ= 0.3 versus H_a: μ< 0.3 using significance level 0.05, we find that the power of this test against an alternative of μ= 0.28 based on a random sample of size n = 40 is 0.808. What impact would using a larger sample size (n = 50) have?

Quizplus · Accepted Answer

Increasing the sample size generally increases the power of a hypothesis test, as it provides more information and reduces the effect of random variation. Therefore, with a larger sample size of 50, the power of the test against an alternative of μ= 0.28 would likely increase. The probability of a Type I error (rejecting the null hypothesis when it is actually true) should remain the same as the significance level is fixed at 0.05.

The Level of Nitrogen Oxides (NOx) in the Exhaust of Cars

The Level of Nitrogen Oxides (NO_x) in the Exhaust of Cars