Question

3. We want to estimate the difference between the mean starting salaries for recent graduates with mechanical engineering and aerospace engineering bachelor’s degrees from an university. The following information is provided:

a) A random sample of 49 starting salaries for mechanical engineering graduates produced a sample mean of $64,650 and a standard deviation of $7,000.

b) A random sample of 36 starting salaries for aerospace engineering graduates produced a sample mean of $63,420 and a standard deviation of $6,830.

(1) Find a 95% confidence interval for the difference between the two mean starting salaries.

(2) Someone made a statement that mechanical engineering new graduates make more money than aerospace engineering new graduates on average at the university. Do you agree with the statement? Explain why.

Answer 1

1)

Level of Significance ,    α =    0.05      
              
Sample #1   ---->   mechanical      
mean of sample 1,    x̅1=   64650.00      
standard deviation of sample 1,   s1 =    7000.000      
size of sample 1,    n1=   49      
              
Sample #2   ---->   aerospace      
mean of sample 2,    x̅2=   63420.00      
standard deviation of sample 2,   s2 =    6830.000      
size of sample 2,    n2=   36      

Degree of freedom, DF=   n1+n2-2 =    83              
t-critical value =    t α/2 =    1.9890   (excel formula =t.inv(α/2,df)          
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    6928.8219              
                      
std error , SE =    Sp*√(1/n1+1/n2) =    1520.9662              
margin of error, E = t*SE =    1.9890   *   1520.97   =   3025.14  
                      
difference of means =    x̅1-x̅2 =    64650.0000   -   63420.000   =   1230.0000
confidence interval is                       
Interval Lower Limit=   (x̅1-x̅2) - E =    1230.0000   -   3025.1406   =   -1795.1406
Interval Upper Limit=   (x̅1-x̅2) + E =    1230.0000   +   3025.1406   =   4255.1406

b)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 >   0

since, confidence interval contains 0, null hypothesis is retained

there is no significant evidence that mechanical engineering new graduates make more money than aerospace engineering new graduates on average at the university