Questions: The Sweet Encounter is a touring international candy festival. The festival's most popular product is rainbow lollipops. Among the 720 products offered at one stop of the tour, 260 were rainbow lollipops. At that stop, the festival promoter took a sample of 45 of the products offered. He found that 19 of those products were rainbow lollipops. For the festival promoter's 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: (Choose one) = (b) Sample proportion: (Choose one) V=

The Sweet Encounter is a touring international candy festival. The festival's most popular product is rainbow lollipops. Among the 720 products offered at one stop of the tour, 260 were rainbow lollipops. At that stop, the festival promoter took a sample of 45 of the products offered. He found that 19 of those products were rainbow lollipops.

For the festival promoter's 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: (Choose one) =
(b) Sample proportion: (Choose one) V=

Transcript text: The Sweet Encounter is a touring international candy festival. The festival's most popular product is rainbow lollipops. Among the 720 products offered at one stop of the tour, 260 were rainbow lollipops. At that stop, the festival promoter took a sample of 45 of the products offered. He found that 19 of those products were rainbow lollipops. For the festival promoter's 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: $\square$ (Choose one) $=$ $\square$ (b) Sample proportion: $\square$ (Choose one) $\mathbf{V}=$ $\square$

Solution

Solution Steps

Step 1: Calculate the Population Proportion (P)

To calculate the population proportion (P), we use the formula $P = \frac{X}{N}$, where $X$ is the number of items of interest in the population and $N$ is the total population size. Substituting the given values, we get $P = \frac{260}{720} = 0.36$.

Step 2: Calculate the Sample Proportion ($\hat{{p}}$)

To calculate the sample proportion ($\hat{p}$), we use the formula $\hat{p} = \frac{x}{n}$, where $x$ is the number of items of interest in the sample and $n$ is the total sample size. Substituting the given values, we get $\hat{p} = \frac{19}{45} = 0.42$.