To study whether the students at a university are satisfied

To study whether the students at a university are satisfied with the food service, a sample of 200 students revealed that 68% of them said they were satisfied with the food service. Test the hypothesis at the 10% level of significance that less than 74% of students are satisfied with the food service.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.74
Ha:   p   <   0.74
As we see, the hypothesized po =   0.74      
As it is given,          
          
po =    0.74      
          
Getting the standard error of po, spo,          
          
spo = sqrt[po (1 - po) / n] =    0.031016125      
          
Getting the z statistic,          
p^ =    0.68      
z = (p^ - po)/spo =    -1.934477641      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.026527214      

significance level =    0.1      

Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.      

There is significant evidence that less than 74% of students are satisfied with the food service. [conclusion]