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. Suppose a follow-up survey showing that 49 of 400 persons now rate Pepsi as being "concerned with my health", calculate the z statistic. (Round your answer to 3 decimal places.)

Answer:The statistic for this case would be given by:[tex]z=\frac{0.18 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=2.67[/tex]  Step-by-step explanation:Infromation providedn=100 represent the random sample selectedX=18 represent the people who rates Pepsi as being "concerned with my health"[tex]\hat p=\frac{18}{100}=0.18[/tex] estimated proportion of people who rates Pepsi as being "concerned with my health" [tex]p_o=0.1[/tex] is the value that reference to comparez would represent the statisticHypothesis to testFor this case we can assume that the interest is check if the proportion of people who rates Pepsi as being "concerned with my health" is equal to 0.1 or not , then the system of hypothesis are:Null hypothesis:[tex]p=0.1[/tex]  Alternative hypothesis:[tex]p \neq 0.1[/tex]  The satistic for this one sample proportion test is given by:[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  Replacing the info given we got:[tex]z=\frac{0.18 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=2.67[/tex]