7 According to a June 2011 Gallop Poll of 8013 people 646 of

7) According to a June 2011 Gallop Poll of 8013 people, 646 of them admitted to shoplifting at least once in the last year. Test the claim that at least 10% of people have shoplifted at least once in the last year.

Solution

7.

Formulating the null and alternatuve hypotheses,          
          
Ho:   p   >=   0.1
Ha:   p   <   0.1

As we see, the hypothesized po =   0.1      
Getting the point estimate of p, p^,          
          
p^ = x / n =    0.080618994      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.00335138      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    -5.782992508      
          
As this is a    1   tailed test, then, getting the p value,  
          
p =    3.66917*10^-9
      

significance level =    0.05      

As P < 0.05, we REJECT THE NULL HYPOTHESIS.      

Thus, there is significant evidence that there is NOT at least 10% of people have shoplifted at least once in the last year. [CONCLUSION]