Question

In a survey of 500 females and 500 male students, 345 and 365 female and male students respectively, reported that they decided to attend college in order to make more money. Is ther population of female students who decided to attend college in order to make more money less than that of male studenst? Conduct the test with a significance level of 0.05.

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 <   0          
                  
sample #1   -----> fro female   
first sample size,     n1=   500          
number of successes, sample 1 =     x1=   345          
proportion success of sample 1 , p̂1=   x1/n1=   0.6900          
                  
sample #2   -----> for male
second sample size,     n2 =    500          
number of successes, sample 2 =     x2 =    365          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.730          
                  
difference in sample proportions, p̂1 - p̂2 =     0.6900   -   0.7300   =   -0.0400
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.7100          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.0287          
Z-statistic = (p̂1 - p̂2)/SE = (   -0.040   /   0.0287   ) =   -1.3938
                  
p-value =        0.0816 [Excel function =NORMSDIST(z)      
decision :    p-value>α,Don't reject null hypothesis               
                  
Conclusion:   There is not enough evidence to conclude that population of female students who decided to attend college in order to make more money less than that of male students