Second Grading 1st Topic: z-test for a Proportion

After our first grading lessons in Advanced Statistics, I almost forgot that there is still the second grading lesson that awaits us. For me, it seemed like we already finished our course. I know that we learned a lot, yet in my own self I can say that lessons for each day can remain into my mind for just a week. My mind can just apply the lessons learned in Stat in just a week or a couple of days more and I can do my best in solving problems with the use of our handouts. This second grading I will try to do my best not to rely on the handouts more but to trust my mind for what it has stored.

The first topic that we discussed for the second grading is all about z-test for a Proportion. I knew that we already forgot about theories by now and we’re now just good in applications and computations. So for the first topic, here is the thought of it and of when we can use it:

A hypothesis test involving a population proportion can be considered as a binomial experiment when there are only two outcomes and the probability of a success does not change from trial to trial. Since the normal distribution can be used to approximate the binomial distribution when np≥ 5 and nq≥ 5, the standard normal distribution can be used to test hypotheses for proportions.

Formula for the z-test for proportions

Here is a sample problem and the step by step process that needs to be done:

From past records, a hospital founds that 37% of all full-term babies born in the hospital weighted more than 7 pounds 2 ounces. This year a sample of 100 babies showed that 23 weight over 7 pounds 2 ounces. At alpha=0.01, is there enough evidence to say the percentage has changed?

The first step is to identify the null and alternative hypothesis. After that, we should identify the claim.

H₀: p = 0.37

H₁: p ≠ 0.37 (claim)

The second step is to identify the Critical Value (CV).

α=0.01, two-tailed test, CV=+2.58

Third step: Solve for the test value using the formula for the z-test for proportions.

Fourth step: Have your decision of rejecting or not rejecting the null hypothesis.

      Reject the null hypothesis, since the test-value falls inside the critical region.

Last step is to summarize the results.

      There is enough evidence to support the claim that the percentage has changed.

Another way to solve is using the P-value. Here is a sample problem:

   There will still be so many lessons to be discussed and we need to get more eager to learn more. We should try to do the best that we can so that our grades will not suffer, for my first grading grade in Advanced Statistics, it is so good, better than what I did expect. Maybe I need to maintain my grade or I should need to have a higher grade than it. I have my dearest gratitude to God that in everything that I do and learn, He was always there to help and to part me His wisdom. May God bless the III-Gold students all throughout school year 2012-2013.

JJJJJJJJJJ

By: Kent Spencer Manalo Mendez