Hello I have some questions about STAT that I want to someon

Hello, I have some questions about STAT that I want to someone can help me. Please give me detailed solutions. Thank you!!

A real estate salesperson claims that 60% of all homeowners move to another house within five years of the time they purchase their fi sample of 144 homeowners, 72 were found to have moved within five years after buying their first house Use a 0.05 level of significance. om

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.6
Ha:   p   =/=   0.6
As we see, the hypothesized po =   0.6      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.5      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.040824829      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -2.449489743      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.014305878      
significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the proportion of all homeowners that move to another house within 5 years from the time they purchased their first house is not 60%. [CONCLUSION]