From the given research, compare the major players better at batting than 20 years ago using five step hypothesis.
Hypothesis testing is a scientific process in which a problem, problem, or opportunity is answered. There is a five-step procedure that is used to reveal a response statistically. This process will assist in looking closer at Major League Baseball data
Research problem/Problem/Opportunity
Major League baseball gives many opportunities to research the game. For this scenario, the present day batting averages will be compared to those from 20 years ago. Therefore, hypothesis testing procedures will help answer the problem, are major league baseball players better at batting now than compared to those 20 years ago?
Five Step Hypothesis Results
The hypothesis testing procedure was used to test the research problem included the following five steps:
1. Status the hypotheses.
2. Choose a level of significance.
3. Set up the decision rule
4. Compute the test statistic. And,
5. Create a decision.
Condition the Hypotheses
When trying to formulate the answer to analyzing the average batting average between today's baseball teams and the baseball teams of 20 years ago, the first step is to formulate a hypothesis. For this scenario, hypotheses were formulated using a right-tailed test based on the statistical problem at hand. The null hypothesis states that the batting averages of today's teams are the same as or lower than the average from 20 years ago. Given this null hypothesis, the alternate hypothesis must state that the batting averages of today's teams are higher than the average from 20 years ago. The hypotheses stated numerically are as follows:
H_{0} = BA ≤ 0.252
H_{1} = BA > 0.252.
Select a Level of Significance
A 95 percent confidence interval is a commonly used to help limit the amount of type I and type II errors; therefore, this confidence interval was used in the testing procedures. The 95% confidence interval leaves a 5% or .05 significance level of rejecting the null hypothesis. In other words, if the resulting calculations fall within the right 5% tail of the data, the null hypothesis would be rejected.
Establish the Decision Rule
Given the alternate hypothesis, it is determined that a right-tailed test needs to be performed. "The decision rule uses the known sampling distribution of the test statistic to establish a threshold called the critical value" (Doane & Seward, 2007). If the test statistic is greater than the critical value, then it falls within the rejection region; thus, the null hypothesis would be rejected. The critical value in this test is determined to be 0.267. Therefore, H_{0} is rejected if the test statistic is greater than 0.267.
find out the Test Statistic
The data set that was used in this hypothesis testing procedure consisted of a sample size of 30. Given the sample size, it is determined that a z-test should be used to test the hypothesis. By using the Excel MegaStat add-in, the test statistic was find outd to be 0.264 (see Appendix B for more results).
Make a Decision
Upon completing the hypothesis test, a decision can be made on whether or not to reject the null hypothesis. Since the test statistic of 0.264 does not fall within the rejection region of the test, the null hypothesis cannot be rejected.
How the Hypothesis Results Answer the Research problem
Since the hypothesis testing did not reject the null hypothesis, the research problem cannot be conclusively answered. The hypotheses can be re-evaluated and more data can be recollected in order to conduct the testing again. The hypothesis testing procedure did reveal that the batting averages of the sample were higher than the average 20 years ago. Though, there was not enough of a difference to state that all batting averages of present day are higher than those of 20 years ago.
The 5-step hypothesis testing procedure scientifically analyzes the data of a sample to compare it to a set figure in order to answer a research problem. While the null hypothesis fails to be rejected, the research problem cannot be answered with certainty. In the scenario with the Major League baseball batting average data, the hypothesis testing was inconclusive.