In a recent poll of 755 randomly selected adults 586 said th

In a recent poll of 755 randomly selected adults, 586 said that it is morally wrong to not report all income on tax returns. Use a 0.05 significance level to test the claim that 75%of adults say that it is morally wrong to not report all income on tax returns. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

Solution

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.75
Ha:   p   =/=   0.75
As we see, the hypothesized po =   0.75      

Getting the point estimate of p, p^,          
          
p^ = x / n =    0.77615894      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.015758946      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.659942285      
          
As this is a    2   tailed test, then, getting the p value,  
          
p =    0.096926064      

significance level =    0.05      

As p > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, there is no significant evidence that not 75% of adults say that it is morally wrong to not report all income on tax returns.