We conduct a simulation to mimic randomly sampling from a population with of college graduates. In the population 62% had student loans. Each sample has 50 graduates in it. What will be the mean of the distribution of sample proportions? Enter a number in decimal form. For example, you would enter 0.50, not 50 or 50%.

The correct answer is 0.069

Explanation:

Solution

Let recall that,

In the population, the number of student that took loans where = 62%

Each samples has graduates of = 50

The next step is to enter a number in decimal form.

Given that,

p = 62% = 0.62

1 - p = 1 - 0.62 = 0.38

Thus,

n = 50

The mean = μ p = p = 0.62

Then,

The standard deviation = б p = √{p (1 - p) / n]

= √[ (0.62 * 0.38) / 50 ] = 0.069

Therefore, the number form is 0.069

mean is 0.62

Explanation:

In statistics, for repeated samples (each with same n), all taken from the same population, when the proportion of interest equals p, then the mean of all p^ should be equal to the population proportion = p.

In this case, all the samples where taken from college graduates and they all have n = 50, then the mean of the distribution of sample proportions will be equal to the population proportion = 62% = 0.62.