It\'s what you keep that matters! What percentage of Company\'s revenue is profi

Question

It's what you keep that matters! What percentage of Company's revenue is profit? Let's consider the insurance industry and the health care industry. Annual profit as a percentage of revenue is shown below for a group of companies in the insurance industry. Names such as New York Life, Prudential, John Hancock, Mutual of Omaha, and so on are included, and the sample size was fourty. For a group of health care organizations, annual profit as percentage of revenue is shown next. Names such Humana, Columbia Health Care, Manor Care, United Health care, and so on are included and the sample size was 30.

b. For 90% confidence, find the margin of error.

d. Examine the confidence interval and explain what it means in this context.

Explanation / Answer

a)

It is the difference of sample means,

X1 - X2 = 4.4 - 4.6 = -0.2 [ANSWER]

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b)

Calculating the standard deviations of each group,              
              
s1 =    1.7          
s2 =    1.4          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    40          
n2 = sample size of group 2 =    30          

Also, sD =    0.370922274          
              
For the   0.9   confidence level, then      
              
alpha/2 = (1 - confidence level)/2 =    0.05          
z(alpha/2) =    1.644853627          

So

Margin of error = z(alpha/2) * sD = 0.610112848 [ANSWER]

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c)

Also,
              
lower bound = [X1 - X2] - z(alpha/2) * sD =    -0.810112848          
upper bound = [X1 - X2] + z(alpha/2) * sD =    0.410112848          
              
Thus, the confidence interval is              
              
(   -0.810112848   ,   0.410112848   ) [ANSWER]

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d)

We are 90% confident that the true mean difference between that annual profit as a percentage of revenue for insurance and health care industries is between -0.810112848% and 0.410112848%.

As 0 is inside this interval, there is no significant difference between the annual profit as a percentage of revenue for insurance and health care industries.

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Hi! I used z distribution because both sample sizes are greater than 30. If you use another method, like a t test, please resubmit this question indicating your desired method. That way we can continue helping you! Thanks!

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