Question

a small community college has a population of 986 students, 252 of whom them are considered non-traditional students. find the population proportion of non-traditional students, as well as the mean and standard deviation of the sampling distribution for samples of size n

Answer 1

The population proportion of non-traditional students is approximately 0.255. The mean and standard deviation of the sampling distribution cannot be calculated without the standard deviation of the population.

Step-by-step explanation:

To find the population proportion of non-traditional students, divide the number of non-traditional students by the total number of students. In this case, there are 252 non-traditional students out of a total population of 986. So the population proportion of non-traditional students is 252/986, which is approximately 0.255.

To find the mean and standard deviation of the sampling distribution for samples of size n, we need to know the standard deviation of the population. Unfortunately, this information is not provided in the question. Without the standard deviation of the population, we cannot calculate the mean and standard deviation of the sampling distribution.

Answer 2

The population proportion of non-traditional students is calculated by dividing the number of non-traditional students (252) by the total student population (986). The mean of the sampling distribution is equal to the population proportion, and the standard deviation of the sampling distribution is found using the formula for proportions with a given sample size n.

Step-by-step explanation:

To find the population proportion of non-traditional students at the small community college with a student population of 986, out of which 252 are non-traditional, you would divide the number of non-traditional students by the total number of students. The proportion (P) is calculated as P = 252 / 986.

As for the mean (μ) and standard deviation (σ) of the sampling distribution of the proportion for samples of size n, they are calculated under the assumption that the population's distribution is approximately normal and that the sample size (n) is sufficiently large, meaning np ≥ 10 and nq ≥ 10 where q = 1 - p.

The mean of the sampling distribution is the same as the population proportion, so μ = P. The standard deviation for the sampling distribution is calculated using the formula σ = √{(P(1 - P)/n)}.

Notice that the actual sample size (n) hasn't been provided, so you will need to substitute the specific value of n whenever you have it to find the standard deviation for a given sample size.