9.4 Full hypothesis test examples  (Page 5/37)

Here is an abbreviate version of the system to solve hypothesis tests applied to a test on a proportions.

Let’s follow a four-step process to answer this statistical question.

1. State the Question : We need to determine if, at a 0.05 significance level, the average conductivity of the selected glass is greater than one. Our hypotheses will be
   1. H ₀ : μ ≤ 1
   2. H _a : μ >1
2. Plan : We are testing a sample mean without a known population standard deviation with less than 30 observations. Therefore, we need to use a Student's-t distribution. Assume the underlying population is normal.
3. Do the calculations and draw the graph .
4. State the Conclusions : We cannot accept the null hypothesis. It is reasonable to state that the data supports the claim that the average conductivity level is greater than one.

1. We need to conduct a hypothesis test on the claimed cancer rate. Our hypotheses will be
   1. H ₀ : p ≤ 0.00034
   2. H _a : p >0.00034

   If we commit a Type I error, we are essentially accepting a false claim. Since the claim describes cancer-causing environments, we want to minimize the chances of incorrectly identifying causes of cancer.

2. We will be testing a sample proportion with x = 172 and n = 420,019. The sample is sufficiently large because we have np = 420,019(0.00034) = 142.8, nq = 420,019(0.99966) = 419,876.2, two independent outcomes, and a fixed probability of success p = 0.00034. Thus we will be able to generalize our results to the population.