Question

random variables and distributions
notation for the population proportion and sample proportion
the plush zoo store sells stuffed animals. the store is running a special on teddy bears this month. one day, the shopkeeper took a sample of stuffed animals at
the store. she found that 5 of the 31 stuffed animals that she sampled were teddy bears. the store had 780 stuffed animals on that day, and 120 of those
stuffed animals were teddy bears.
for the shopkeepers sample, find and write with proper notation the sample proportion and population proportion of stuffed animals that were teddy bears.
write the proportions as decimals (not percentages) rounded to two decimal places.
(a) sample proportion: select =
(b) population proportion: select =

Explanation:

Step1: Find the sample proportion

The formula for sample proportion $\hat{p}$ is $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes in the sample and $n$ is the sample size. Here, $x = 5$ (number of teddy - bears in the sample) and $n=31$ (sample size).
$\hat{p}=\frac{5}{31}\approx0.16$

Step2: Find the population proportion

The formula for population proportion $p$ is $p=\frac{X}{N}$, where $X$ is the number of successes in the population and $N$ is the population size. Here, $X = 120$ (number of teddy - bears in the population) and $N = 780$ (population size).
$p=\frac{120}{780}=\frac{2}{13}\approx0.15$

Answer:

(a) Sample proportion: $\hat{p}=0.16$
(b) Population proportion: $p = 0.15$