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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.)

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Answer:

z statistic equals 1.5

Step-by-step explanation:

z-score can be calculated using the formula

[tex]z=\frac{p(s)-p}\sqrt{\frac{p(1-p)}{N}}[/tex] where

  • p(s) is the proportion of follow-up survey ([tex]\frac{49}{400}[/tex])
  • p is the base proportion (0.10)
  • N is the sample size of follow-up survey (400)

putting these numbers in the formula we get:

[tex]z=\frac{0.1225-0.1}\sqrt{\frac{0.1*0.9}{400}}[/tex] = 1.5