An organizational psychologist wants to know if workers\' health would improve i

Question

An organizational psychologist wants to know if workers' health would improve if a company gave workers extra days off. All workers take a standard physical exam twice a year and are given an overall health rating with higher scores indicating better health. The psychologist selected five workers at random, arranged to have them receive an additional 2 days off every month over the period between health exams, and then compared the health scores on the two exams. Using the .01 significance level, do the scores in the table below support the notion that having extra days off improves health?

Health Rating Before and After Period of Extra Days Off    

Worker            Before             After                          

A                     75                    81

B                     66                    65

C                     44                    46

D                     80                    88

E                      89                    87                               

A) What is the appropriate test for this data?

B) Conduct the appropriate hypothesis test by hand. Follow the five steps of hypothesis testing and provide a drawing.

C) Give an interpretation of this data (one sentence conclusion of the hypothesis test that should be free of statistical jargon) and report the statistics in APA format.

D) Explain how you found the characteristics of the comparison distribution. In your explanation, be sure to use the names of the concepts. For example, if you are calculating variance for the distribution of means call it that. Do not simply say “that number”.

Mbefore = 70.80

Mafter= 73.40

SSbefore = 1174.80

SSafter = 1277.20

Mdifference = 2.60

SSdifference = 75.20

Difference = After – Before

Explanation / Answer

Part (a)

Appropriate test for this data is a paired t-test (and NOT two-sample t-test) since the subjects of the experiment are the same 5 employees and what is desired to be tested is the improvement or otherwise. ANSWER

Part (b)

Let X = Health rating before 2 days’ extra off and Y = Health rating after 2 days’ extra off.

Then, D = Y – X, is the characteristic of interest.

We assume D ~ N(µ, 2).

H0: µ = 0 (i.e., extra 2 days’ off does not enhance health rating)   Vs

HA: µ > 0 (i.e., extra 2 days’ off enhances health rating)

Test Statistic: t = (n)Dbar/SD(D), where n = sample size (5), Dbar = sample average of D and SD(D) = sample standard deviation of D.

Under H0, t ~ tn – 1

Decision criterion: Reject H0, at % level of significance if tcal (i.e., calculated value of t) > tcrit (i.e., upper % point of tn-1)

Computations :

SD(D) = {SSDifference /(n - 1)} = (75.20/4) = 4.3358

t = (5)x2.60/4.3358 = 1.341

Given = 0.01, using Excel Function, t4, 0.01 = 3.347

Since 1.341 < 3.347, H0 is accepted. ANSWER

Part (c)

Conclusion: There is no evidence to suggest that giving 2 days extra off would enhance health rating. ANSWER

Part (d)

The characteristic of study is the difference in health rating for each employee and not the difference in their averages. ANSWER

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