*1. **Hypothesis*
Through application of the variables in the provided Happiness and Engagement dataset, a good hypothesis would be that an improvement in positive relationships with an employees’ direct supervisor would improve the workplace happiness.
*2. **Null Hypothesis *
An improvement in positive relationships with an employees’ direct supervisor will have no effect on the workplace happiness.
*3. **Alternate Hypothesis *
Employee’s having a good relationship with their supervisor does not mean that they will be happier in the workplace.
*4. **Statistical Analysis*
The variables in the dataset are from a single population and are observed from the single population. I believe that the paired *t* test would be the most appropriate technique of statistical analysis to be applied in this scenario. A paired *t* test mainly contrasts two sample means from a single population, different to a *t* test, which compares two detached populations. In this case, a supervisor’s relationship with their employee and workplace happiness are two observations compared in a single population.

*5. **t-test Analysis*
When I ran the t test with two samples of assumed equal variances, I got the t test statistic of -19.90 along with the prospect and perilous values for both one and two-tailed tests. I was able to find on the one-tailed critical value of t that the test is significant at p = 1.6719 -36. If the output on this t test was measured against the equal significance in the social sciences again, the argument would be that the results do show a significance. The standard nominal level of significance is the social sciences is 0.05 and the tests significance at p is equal to 1.6719 -36, then this permits additional examination between workplace happiness and the affiliation of an employee and the direct supervisor.

t-Test: Two-Sample Assuming Equal Variances

Supervisor
Happiness
Mean
2.5
7.4
Variance
1.030612245
2
Observations
50
50
Pooled Variance
1.515306122
Hypothesized Mean Difference
0
df
98
t Stat
-19.90287866
P(T<=t) one-tail 1.67192E-36 t Critical one-tail 1.660551217 P(T<=t) two-tail 3.34383E-36 t Critical two-tail 1.984467455References Jackson, S. L. (2017). *Statistics plain and simple* (4th ed.). Boston, MA: Cengage Learning.