In a recent survey 10 percent of the participants rated Peps

In a recent survey, 10 percent of the participants rated Pepsi as being \"concerned with my health.\" PepsiCo\'s response included a new \"Smart Spot\" symbol on its products that meet certain nutrition criteria, to help consumers who seek more healthful eating options.

a. Suppose a follow-up survey showing that 13 of 100 persons now rate Pepsi as being \"concerned with my health\", calculate the z statistic. (Round your answer to 3 decimal places.)

b. At = 0.05, would a follow-up survey showing that 13 of 100 persons now rate Pepsi as being \"concerned with my health\" provide sufficient evidence that the percentage has increased?

Solution

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 =    0.13      
          
Getting the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n] =    0.03      
          
Getting the z statistic,          
          
z = (p^ - po)/sp =    1.000 [ANSWER, PART A]

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As this is a    1   tailed test, then, getting the p value,  
          
p =    0.317310508      
significance level =    0.05      

Comparing p and the significance value, we   FAIL TO REJECT THE NULL HYPOTHESIS.      

WE HAVE NO SUFFICIENT EVIDENCE THAT THE PERCENTAGE INCREASED.