Question

A group of Industrial-Organizational psychologists is examining how perceptions of the quality of physical facilities at a workplace play a role in perceptions of workplace cohesion. They predict that employees working under sub-standard conditions experience greater workplace cohesion, due to the employees’ strong agreement that the conditions are unacceptable. The researchers collect data on perceptions of workplace cohesion (scale: 0-100) for employees who work under sub-standard conditions and employees who work under conditions that are above average. The data are summarized below.

                                                Sub-standard   Above average       Difference (sub-above)

   88.00 69.00 19.00

                     s                          7.00 12.00 4.00

                     n                         58.00 70.00 58.00

                                                    

1. First, the researchers test the hypothesis that employees working in sub-standard conditions experience greater workplace cohesion than employees who work in above average conditions. Conduct the appropriate statistical test and state your conclusion based on the data.

Type of test: ____________________________________________________________

Null & alternative hypotheses (either words or symbols is fine):

H₁:           

H₀:                                                                                                                       

Formula(s):

Calculations:

                                                                                                                    

t =                                t_critical =                                      df =   

Answer 1

Type of test : One sample t test

To test null hypothesis against alternative hypothesis

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if p-value < 0.05 or

Now,

The value of the test statistic

and

and p-value =

Since p-value < 0.05, so we reject H₀ at 5% level of significance and the test is significant and we can conclude that employees working under sub-standard conditions experience significantly greater workplace cohesion than the population of all workers (whose mean score is 73)