158k views
4 votes
The candy machine Suppose a large candy machine has 15% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion $ of orange candies.

1 Answer

4 votes

The proportion of orange candies in the sample would be a random variable, denoted as $. The true proportion of orange candies in the candy machine is 0.15, and the mean of $ is also 0.15. The standard deviation of $ is given by the formula:

$\sqrt{\frac{p(1-p)}{n}}$

where p is the true proportion of orange candies in the candy machine and n is the sample size. In this case, the standard deviation of $ is

$\sqrt{\frac{0.15(1-0.15)}{25}}$

$\approx$ 0.03

This means that the sample proportion of orange candies is likely to be close to the true proportion of orange candies in the candy machine, but there is a certain amount of variability or uncertainty associated with the estimate.

User Kacper Madej
by
6.9k points