Answer:
The statistic for this case would be given by:
Step-by-step explanation:
Infromation provided
n=100 represent the random sample selected
X=18 represent the people who rates Pepsi as being "concerned with my health"
estimated proportion of people who rates Pepsi as being "concerned with my health"
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:
Alternative hypothesis:
The satistic for this one sample proportion test is given by:
(1)
Replacing the info given we got:
X = amount of the 18% solution
y = amount of the 40% solution
we know the 18% solution has only 18% of alcohol, the rest is maybe water or something, now, how many liters is 18%? well, 18% of anything is just (18/100) * anything, so, 18% of x is just (18/100) *x or 0.18x, and that's how many liters are there.
likewise, how many liters are there in the 40% solution? well, (40/100) * y, or 0.4y, that many.
we know the mixture has to yield 10 liters at 20% alcohol, how many liters of only alcohol is that? well, (20/100) * 10, or 2 liters.
how much of the 40% solution? well y = 10 - x
