Question

In a recent poll of

740740

randomly selected? adults,

588588

said that it is morally wrong to not report all income on tax returns. Use a

0.050.05

significance level to test the claim that

7575?%

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. test statistic z- round to 2 decimal places

Answer 1

p(hat)=   588/740=0.7946          
n=   740          
      
         
...........      two tail test  
alpha=   0.05          
      
Test Statistics              
Z=   (p(hat)-P)/sqrt(p*q/n)
=(0.7946-0.75)/sqrt(0.75*0.25/740)
=2.8015

rounded z statistics= 2.80
P-value=P(Z>2.8015)=0.002542935   (this p-value is for one tail to get p-value for two tail we need to multiply it by 2.)       
rounded p-value=2*0.00254=0.00508        

Decision making               
P-value ? Alpha   Reject H0          
0.00508<0.05              
      
there is enough evidence to support the claim that adults who says it is morally wrong to not report all income tax returns is different from 75%.

OR
there is not 75% of adults say that it is morally wrong to not report all income on tax returns.

when we reject null hypothesis alternate hypothesis become true.
.......................
you can ask any doubt in comment.