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 $\hat{p}$.