Question

Jeanette and Evelyn, of Noh Mommies! Medical Group found that the mean annual earnings of pharmacists in the US are $230,000 and those of pediatricians to be $225,000. Suppose that these results are based on a random sample of 300pharmacistsand 400 pediatricians and that the population standard deviations are $28,000 and $32,000, respectively.

a. What is the standard error? (3pts.)

b.Test the claim, using a 1% level of significance, that the mean annual earnings of pharmacists is greater than that of pediatricians.(6pts.)

c.Construct a 98% confidence interval for the difference between the meanannual earnings of pharmacists and pediatricians.(4pts.)

Answer 1

a)

sample #1   ------->              
mean of sample 1,    x̅1=   230000          
population std dev of sample 1,   σ1 =    28000          
size of sample 1,    n1=   300          
                  
sample #2   --------->              
mean of sample 2,    x̅2=   225000          
population std dev of sample 2,   σ2 =    32000          
size of sample 2,    n2=   400          
                  
difference in sample means = x̅1 - x̅2 =    230000   -   225000   =   5000
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    2274.4963          

..............

b)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 > 0
      
Level of Significance ,    α =    0.01

Z-statistic = ((x̅1 - x̅2)-µd)/SE =    5000   /   2274.4963   =   2.1983
                        
                  
p-value =        0.0140   [excel function =NORMSDIST(z)]      
Desison:   p-value>α , Do not reject null hypothesis              

...............

c)

Level of Significance ,    α =    0.02          
z-critical value =    Z α/2 =    2.3263   [excel function =normsinv(α/2) ]      
                  
std error , SE =    √(σ1²/n1+σ2²/n2) =    2274.4963          
margin of error, E = Z*SE =    2.3263   *   2274.496   =   5291.2696
                  
difference of means = x̅1 - x̅2 =    230000   -   225000   =   5000.000
confidence interval is                   
Interval Lower Limit= (x̅1 - x̅2) - E =    5000.000   -   5291.270   =   -291.2696
Interval Upper Limit= (x̅1 - x̅2) + E =    5000.000   +   5291.270   =   10291.2696

.................

THANKS

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