In a recent poll of 755 randomly selected adults 588 said th

In a recent poll of 755 randomly selected adults. 588 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. Identify the correct null and alternative hypotheses. Choose the correct answer below. The test statistic is z = . (Round to two decimal places as needed.) The P-value is . (Round to four decimal places as needed.)

Solution

POPULATION PROPORTION Z TEST          
          
Formulating the null and alternatuve hypotheses,          
          
Ho:   p   =   0.7
Ha:   p   =/=   0.7 [OPTION D]

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As we see, the hypothesized po =   0.7      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.778807947      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.016677701      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    4.73 [ANSWER, ITEM 2]

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As this is a    2   tailed test, then, getting the p value,  
          
p =    1.14861E-06 [ANSWER, ITEM 3]

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significance level =    0.01      
Comparing p and the significance value, we   REJECT THE NULL HYPOTHESIS.