In a recent poll of 755 randomly selected adults, 586 said that it is morally wr

Question

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 0.01 significance level to test the claim that

70% 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.

What is the test statistic___

What is the p-value ____

Explanation / Answer

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.7
Ha:   p   =/=   0.7
As we see, the hypothesized po =   0.7      
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] =    0.016677701      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    4.566513244   [ANSWER, TEST STATISTIC]  
          
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As this is a    2   tailed test, then, getting the p value,  
          
p =    4.95904E-6   [ANSWER, P VALUE]

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As P < 0.01, we REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence that the true population proportion of adults who say that it is morally wrong to not report all income on tax returns is not 0.70 at 0.01 level. [CONCLUSION]

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