Answer:
Step-by-step explanation:
Hello!
The objective is to compare the proportion of male and female students that are in favor of retaining the penny as a form of currency. Two groups of students were surveyed, the study variables are:
X₁: number of female students of the BYU-Idaho out of 116, that are in favor of retaining the penny as a form of currency.
X₂: number of male students of the BYU-Idaho out of 137, that is in favor of retaining the penny as a form of currency.
These two variables are discrete, and they follow the binomial criteria:
The number of observations of the trial is fixed and there are only two possible observations: success: the student is on the favor, failure: the student is against it.
Each observation in the trial is independent, this means that none of the trials will affect the probability of the next trial.
The probability of success in the same from one trial to another.
So we can say that
X₁~Bi(n₁;p₁)
X₂~Bi(n₂;p₂)
To study the difference between both population proportions through a hypothesis test or a Confidence Interval you theed to apply the Central Limit theorem and approximate the distribution of both sample proportions to normal. For that the sample sizes have to be big enough, as a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.
n₁ and n₂ ≥ 30, in this case, n₁= 116 and n₂=137
So the conditions are meet to estimate the difference per CI and test it through a hypothesis test.
I hope this helps!
