Question

A researcher is interested in determining if the more than two thirds of students would support making the Tuesday before Thanksgiving a holiday. The researcher asks 1,000 random selected students if they would support making the Tuesday before Thanksgiving a holiday. Seven hundred students said that they would support the extra holiday.
Define the parameter.

a. p = the population proportion of UF students who would support making the Tuesday before Thanksgiving break a holiday.

b. phat = the sample proportion of 700 UF students who would support making the Tuesday before Thanksgiving break a holiday.

c. phat = the population proportion of UF students who would support making the Tuesday before Thanksgiving break a holiday.

d. p = the population proportion of 700 UF students who would support making the Tuesday before Thanksgiving break a holiday.

Answer 1

Answer:

a. p = the population proportion of UF students who would support making the Tuesday before Thanksgiving break a holiday.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are in favor of making the Tuesday before Thanksgiving a holiday, or they are against. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

So, the binomial probability distribution has two parameters, n and p.

In this problem, we have that $n = 1000$ and $p = \frac{700}{1000} = 0.7$. So the parameter is

a. p = the population proportion of UF students who would support making the Tuesday before Thanksgiving break a holiday.