Statistical Test for Significantly Different Sample Means

Independent – Samples t-Test The Independent sample t-test is among the group of inferential statistical test. This test seeks to compare the means of two unrelated samples in a survey. The t-test determines whether the mean of the two sample is significantly different statistically (Paul & Garg, 2014). According to Ruane (2005) for this test to be undertaken, both samples must have scores with one carrying nominal scale and another one a numerical scale. The sample carrying the nominal is a grouping variable and is the independent variable.

The sample with the numerical scale is a test variable and is the dependent variable (Ruane, 2005). This paper seeks to determine the statistical significance between the means of work shift (day and night shift) and the mean of the number of widgets produced in either shifts. This will be undertaken by use of the independent sample t-test. The work shift is the independent variable that defines the distinct group each worker belongs to. The number of widgets produced is the dependent variable given as a quantitative figure.

Research Question Is there a statistically significant mean between the widgets produced by employees working in the day and night shifts? Hypotheses H0: There is no statistically significant difference in the mean of widgets produced by employees working in the day and night shifts. H1: There is a statistically significant difference in the mean of widgets produced by employees working in the day and night shifts. Variables The independent variable is the working shifts (day and night shifts) while the dependent variable is the number of widgets produced.

Results To determine whether those working in the day shift produce a significantly different number of widgets compared to the night shift workers, an independent sample t-test was conducted. From the group statistics table, the mean number of widgets produced in the day shift is 45.20 while for the day shift is 22.07. The deference between these two values is 23.13. No violation are noted in evaluation of the Levenes Test (P=0.881). The result indicates 0.022 in the 2 tailed significance level where it is less than 0.05 (alpha).

This result shows that the difference between the mean of the two groups’ is a significantly different statistically. The test leads to the conclusion that the mean difference between widgets produced by employees working in the day and night shifts is significantly different statistically. The statistically significant mean differences for the two variables suggest that one of the shifts is more productive than the other one. The determination of the shift that is more productive than the other facilitated by a box plot diagram.

Figure 1 below shows a box plot giving the number of widgets produced by each work shift. The box plot depict that the employees working.