Question

the sweet encounter is a touring international candy festival. the festivals most popular product is rainbow lollipops. at one stop of the tour, 19 out of every 60 products offered are rainbow lollipops. at that stop, the festival promoter took a sample of the products offered. he found that 25 of the 96 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: =
(b) sample proportion: =

Explanation:

Step1: Calculate population proportion

Population proportion \( p=\frac{\text{Number of rainbow lollipops in population}}{\text{Total number of products in population}} \). Here, \( p = \frac{19}{60}\approx0.32\)

Step2: Calculate sample proportion

Sample proportion \( \hat{p}=\frac{\text{Number of rainbow lollipops in sample}}{\text{Total number of products in sample}} \). Here, \( \hat{p}=\frac{25}{96}\approx0.26\)

Answer:

(a) Population proportion: \( p = 0.32\)
(b) Sample proportion: \( \hat{p}=0.26\)