Question

the sweet encounter is a touring international candy festival. the festivals most popular product is rainbow lollipops. at one stop of the tour, 17 out of every 53 products offered are rainbow lollipops. at that stop, the festival promoter took a sample of the products offered. he found that 26 of the 82 products offered in his sample were rainbow lollipops. for the festival promoters sample, find and write with proper notation the population proportion and sample proportion of products offered that were rainbow lollipops. write the proportions as decimals (not percentages) rounded to two decimal places. (a) population proportion: select = (b) sample proportion: select =

Explanation:

Step1: Define population proportion

The population proportion $p$ is the proportion of rainbow - lollipops in the entire set of products offered at the stop. Given that 17 out of every 53 products are rainbow lollipops, we calculate $p=\frac{17}{53}$.
$p=\frac{17}{53}\approx 0.32$

Step2: Define sample proportion

The sample proportion $\hat{p}$ is the proportion of rainbow - lollipops in the sample. Given that 26 out of 82 products in the sample are rainbow lollipops, we calculate $\hat{p}=\frac{26}{82}$.
$\hat{p}=\frac{26}{82}\approx 0.32$

Answer:

(a) $p = 0.32$
(b) $\hat{p}=0.32$