A. Reformulated Two-Sample Quantitative Hypothesis
The reformulated two-sample quantitative hypothesis will be: The mean performance of the performance of employees' that have undergone on the job training is different from the mean performance of employees that have not undergone on the job training. The two-sample hypothesis test presents data collected from two populations. The first population is that of employees that have undergone on-job training, while, the second data-set is the population of employees that have not undergone on-job training. The research question does not seek to investigate which mean is small or larger than the other but instead if the means are the same or not.
The null hypothesis will be; the mean of employees' that have undergone on-job training is equal to the mean of employees that have not undergone on-job training. Therefore it can be represented as shown as µ 1 = µ 2 (equation 1). Where: µ1 is the mean performance of employees that have undergone on-job training while µ 2 is the mean performance of employees that have not undergone on-job training. The alternate hypothesis will be: The mean performance of employees that have undergone on-job training is not the same as the mean performance of employee that has not undergone on-job training. Thus, presented as µ 1 ≠ µ 2 (equation 2).
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The type I error will result from the false rejection of the null hypothesis. Hence, falsely conclude that the mean performance of employees that have undergone on-job training is the same as those that have not undergone on-job training. The type II error, on the other hand, is the false acceptance of the null hypothesis. Such as a false conclusion that the mean of employees that have undergone on-job training is different from the mean of those that have not undergone on-job training.
A p -value of 0.01 indicates that there is a 1% chance that the acceptance or rejection of non-similarity of the mean performance employees with on-job training will be false. A p -value of 0.02, on the other hand, increases the risk to 2%. As such, there is a 2% risk of accepting or rejecting the non-similarity of the two means.
B. The Effect of Increasing the Sample to Three or More
If the design is formulated to have three or more samples, it will be inaccurate to use standard tools for testing a single population hypothesis or two-sample hypothesis test. For instance, the pooled t-test requires that the samples to have a similar variance. It may not always be the case for three or more samples. As such, the Turkey HSD or Turkey –Kramer will be more appropriate. The turkey HSD overcomes the shortcomings of using the individual p-values of the specific samples in determining their relations. It, therefore, compares the differences of means of the samples by dividing the absolute value of the mean by the standard error of the mean.
