In October the campus bookstore asked a random set of freshm

In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test? Freshman Seniors Sample size 60 40 Sample Mean $280 $290 std. dev. $47 $58

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    280          
X2 =    290          
              
Calculating the standard deviations of each group,              
              
s1 =    47          
s2 =    58          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    60          
n2 = sample size of group 2 =    40          

Also, sD =    10.99621147          
              
Thus, the z statistic will be              
              
z = [X1 - X2 - uD]/sD =    -0.909404119   [ANSWER]

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As this is a two tailed test, a positive answer can also do, z = 0.909404, as the answer really depends on convention.