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To solve this problem, let’s break it down into two parts:

### Given Data:
1. **Population**: 960 products.
2. **Number of Rainbow Lollipops in the Population**: 290.
3. **Sample Size**: 60 products.
4. **Number of Rainbow Lollipops in the Sample**: 14.

### Solution:

#### (a) Population Proportion
The **population proportion** (\( p \)) is the ratio of rainbow lollipops in the entire population:
\[
p = \frac{\text{Number of Rainbow Lollipops in Population}}{\text{Total Population Size}} = \frac{290}{960}
\]
Calculating this:
\[
p = 0.3021 \approx 0.30 \quad \text{(rounded to two decimal places)}
\]

#### (b) Sample Proportion
The **sample proportion** (\( \hat{p} \)) is the ratio of rainbow lollipops in the sample:
\[
\hat{p} = \frac{\text{Number of Rainbow Lollipops in Sample}}{\text{Sample Size}} = \frac{14}{60}
\]
Calculating this:
\[
\hat{p} = 0.2333 \approx 0.23 \quad \text{(rounded to two decimal places)}
\]

### Answers:
- **(a) Population proportion (\( p \))** = 0.30
- **(b) Sample proportion (\( \hat{p} \))** = 0.23

Would you like further details on this solution or have any questions?

#### Related Questions:
1. How is a sample proportion different from a population proportion?
2. Why do we round proportions to two decimal places in statistics?
3. What impact does sample size have on the accuracy of a sample proportion?
4. How can we determine if the sample is representative of the population?
5. What statistical methods could verify the accuracy of the sample's proportion?

#### Tip:
Always differentiate between sample and population notations: population proportion is \( p \), while sample proportion is \( \hat{p} \).

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.

Learn how to find the population and sample proportions of rainbow lollipops offered at a festival stop. This example includes the correct notation and step-by-step calculations, rounded to two decimal places, for a sample of 60 products and a population of 960.

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