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.

Suppose a follow-up survey shows that 18 of 100 persons now rate Pepsi as being "concerned with my health".

Calculate the z statistic. (Round your answer to 2 decimal places.)

Answer 1

The statistic for this case would be given by:

`z=\frac{0.18 -0.1}{\sqrt{(0.1(1-0.1))/(100)}}=2.67`

Explanation:

Infromation provided

n=100 represent the random sample selected

X=18 represent the people who rates Pepsi as being "concerned with my health"

`\hat p=(18)/(100)=0.18` estimated proportion of people who rates Pepsi as being "concerned with my health"

`p_o=0.1` is the value that reference to compare

z would represent the statistic

Hypothesis to test

For 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:
`p=0.1`

Alternative hypothesis:
`p \\eq 0.1`

The satistic for this one sample proportion test is given by:

`z=\frac{\hat p -p_o}{\sqrt{(p_o (1-p_o))/(n)}}` (1)

Replacing the info given we got:

`z=\frac{0.18 -0.1}{\sqrt{(0.1(1-0.1))/(100)}}=2.67`