In a recent survey, 10 percent of the participants rated Pepsi as being \"concer
ID: 3437822 • Letter: I
Question
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?
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?
Explanation / Answer
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.
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