1. The Bureau of Labor Statistics shows that the average insurance cost to a com

Question

1. The Bureau of Labor Statistics shows that the average insurance cost to a company per employee per hour is $1.84 for managers and $1.99 for professional specialty workers. Suppose these figures were obtained from 14 managers and 15 professional specialty workers and their respective standard deviations are $0.38 and $0.51. Assume that such insurance costs are normally distributed in the population. Test whether there is a significant difference in the hourly rates employers pay for insurance between managers and professional specialty workers. Use a 2% level of significance.

a. T =

Ho: Ha:

b. p =

c. Conclusion

d. Interpretation in the context of this variable:

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0   [ANSWER]

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At level of significance =    0.02          

As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    1.84          
X2 =    1.99          
              
Calculating the standard deviations of each group,              
              
s1 =    0.38          
s2 =    0.51          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    14          
n2 = sample size of group 2 =    15          
Thus, df = n1 + n2 - 2 =    27          
Also, sD =    0.166295778          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -0.902007267   [ANSWER, t test staistic]

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b)
              
where uD = hypothesized difference =    0          
              
Also, using p values, as this is two tailed,              
              
p =    0.375029622   [ANSWER, P VALUE]

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c)      
              
As P > 0.02,   WE FAIL TO REJECT THE NULL HYPOTHESIS.          

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d)

There is no significant difference in the hourly rates employers pay for insurance between managers and professional specialty workers. [CONCLUSION]

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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