# Hypothesis Testing and Two-Group t Tests

Running Head: Statistics Project Part 2 1

Statistics Project Part 2 3

Statistics Project Part 2

Hypothesis Testing and Two-Group t Tests

Nasser Y Miranda

University of Phoenix

August 4th, 2018

Hypothesis for the Happiness and Engagement Dataset

Hypothesis: Are individuals who have a great relationship with their supervisors likely to be completely happy at their workplace?

Null hypothesis (H0): Individuals having a great relationship with their supervisors are likely to be completely happy at their workplace.

Alternative hypothesis (H1): Individuals having a great relationship with their supervisors are not likely to be completely happy at their workplace.

Justification from the Statistical Analysis

In this case, an independent samples t-test would be of great importance since it compares two mean showing their differences. Moreover, this statistical analysis shows the measure of significance these differences have. The findings enable one to be in a position of knowing whether or not these differences could have resulted from chance (Anderson, 2011).

Independent samples T-Test

 t-Test: Paired Two Sample for Means Relationship Happiness Mean 2.5 7.4 Variance 1.030612245 2 Observations 50 50 Pearson Correlation 0.611237131 Hypothesized Mean Difference 0 df 49 t Stat -30.67885265 P(T<=t) one-tail 6.0097E-34 t Critical one-tail 1.676550893 P(T<=t) two-tail 1.20194E-33 t Critical two-tail 2.009575237

Interpretation for the results

For a two-tailed test, the null hypothesis is rejected when t Stat > t Critical (D’Agostino, 2017). In this case -30.67885265 < 2.009575237 indicating that we should accept the null hypothesis. This shows that it is correct to say that Individuals having a great relationship with their supervisors are likely to be completely happy in their workplace. In cases like this, where there is a negative t-value, there is a reversal in the effect’s directionality. However, this does not have bearing on the significance of the group’s differences (Macisaac et al., 2015). From the dataset, it is clearly seen that the individuals who have a great relationship with their supervisors have a high score of happiness. Organizations should consider embracing and emphasizing teamwork which not only keeps the employees happy but also give them a high retention rate.

 Gender Age Supervisor Telecommute Coworkers Happiness Engagement Overall Rating 2 32 4 1 3 9 10 19 2 29 4 1 2 8 9 17 1 26 4 1 2 8 8 16 1 39 4 1 3 9 8 17 2 35 4 1 2 8 8 16 1 32 4 2 2 8 8 16 1 40 4 1 2 9 8 17 2 27 4 1 1 8 7 15 2 34 4 1 3 9 9 18 2 33 3 1 2 7 8 15 2 36 3 1 2 8 7 15 1 28 3 1 3 9 8 17 1 34 3 2 3 8 8 16 2 27 3 1 2 7 9 16 2 37 3 1 2 9 7 16 1 29 3 2 2 7 8 15 1 29 3 1 2 9 7 16 2 36 3 1 3 9 9 18 1 30 3 1 2 7 7 14 1 27 3 2 3 9 9 18 2 38 3 1 2 8 8 16 2 28 3 1 2 9 9 18 1 35 3 1 2 7 7 14 2 29 3 1 2 8 8 16 1 30 3 1 2 9 9 18 1 30 3 1 2 7 8 15 1 25 2 1 2 5 8 13 2 32 2 1 2 6 8 14 2 37 2 1 1 7 9 16 1 30 2 1 1 6 7 13 2 30 2 1 2 8 7 15 2 31 2 1 3 8 8 16 1 34 2 1 1 5 6 11 1 29 2 2 2 7 8 15 1 35 2 2 3 9 9 18 2 37 2 1 2 8 9 17 1 27 2 1 1 4 6 10 2 25 2 2 2 9 8 17 2 29 2 1 2 8 8 16 2 35 2 2 1 6 6 12 1 29 1 1 2 7 8 15 1 39 1 1 1 4 5 8 1 27 1 1 1 5 4 9 2 31 1 1 1 7 5 12 2 38 1 1 1 6 8 14 1 40 1 1 1 6 8 14 2 38 1 1 2 6 8 14 1 34 1 1 2 8 7 15 2 34 1 2 1 7 5 12 2 25 1 1 1 5 6 11

References

Anderson, T. W. (2011). The statistical analysis of time series(Vol. 19). John Wiley & Sons.

D’Agostino, R. (2017). Goodness-of-fit-techniques. Routledge.

Macisaac, R. L., Khatri, P., Bendszus, M., Bracard, S., Broderick, J., Campbell, B., … & Diener, H. C. (2015). A collaborative sequential meta-analysis of individual patient data from randomized trials of endovascular therapy and tPA vs. tPA alone for acute ischemic stroke: T h R omb E ctomy A nd t PA (TREAT) analysis: statistical analysis plan for a sequential meta-analysis performed within the VISTA-Endovascular collaboration. International Journal of Stroke, 10(SA100), 136-144.