July 25,2012-Lesson on z-test for the Mean

I can’t really digest all of our previous lessons because just these weeks, I always have my early morning and late afternoon migraines.. Just like in my advanced Stat., we have our lesson on z-test and t-test for the mean. These lessons need so much attentiveness in order for me to analyzed and have the correct decision in my answer such as rejecting or not rejecting the null hypotheses and on having my conclusion.

I just don’t really mind my migraine because I need to fully understand our lesson.

Here is one of the problems that we had:

A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistant professors has a mean salary of $43,260. At  α=0.05, test the claim that assistant professors earn more than $42,000 a year. The standard deviation of the population is $5,230.

In order for us to answer problems like this, we should need to follow these 5 steps:

Step 1: State the hypotheses and identify the claim.

Null Hypotheses (H₀):    µ ≤ $42,00     and

Alternative Hypotheses (H₁):      µ > $42,000 (claim)

Step 2: Find the critical value. Since α=0.05 and the test is a right-tailed test, the critical value is z=1.65.

Step 3: Compute the test value.

 Step 4: Make the decision. Since the test value, 1.32 is less than the critical value 1.65, and is not in the critical region, the decision is “Do not reject the null hypothesis”.

Step 5: Summarize the results. There is not enough evidence to support the claim that assistant professors earns more on average than $42,000 a year.

Even though the sample mean, $43,000, is higher than the hypothesized population mean of $42,000, it is not significantly higher. Hence, the difference may due to chance.

It should be noted that when the null hypothesis is not rejected, it cannot be accepted as true. There is merely not enough evidence to say that it is false. This guideline may sound a little confusing, but the situation is analogous to a jury trial. The verdict is either guilty or not guilty and is based on the evidence presented. If a person is judged not guilty, it does not mean that the person is proved innocent; it only means that there is enough evidence to reach the guilty verdict.

By: Kent Spencer M. Mendez