In a random sample of 175 drivers 93 report that they still

In a random sample of 175 drivers 93 report that they still talk on the cell phone while driving Without the use of a hands free device. Set up a hypothesis test to test the claim that the majority of drivers (more than 50%) talk on the cell phone while driving without the USO of a hands free device.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   <=   0.5
Ha:   p   >   0.5
As we see, the hypothesized po =   0.5      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.531428571      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.037796447      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    0.831521841      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    0.202839448      

If we set the significance level =    0.05      

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

Thus, there is no sufficient evidence to conclude that more than 50% talk on cellphone while driving without the use of the hands free device.