To solve this, we need to find both the population proportion and the sample proportion of plants that were cacti. Let's break it down.

Population Proportion:

The population proportion is given by the ratio of the number of cacti in the entire population of plants (based on the information about the expo). We know that:

• 38 out of every 61 plants were cacti at the expo.

The population proportion is the ratio of cacti to the total number of plants:

$\text{Population Proportion} = \frac{38}{61}$

Let's calculate that:

$\text{Population Proportion} = \frac{38}{61} \approx 0.623$

Rounded to two decimal places, the population proportion is 0.62.

Sample Proportion:

The sample proportion is based on the organizer's sample. The sample size is 91 plants, and 50 of these plants were cacti. The sample proportion is the ratio of cacti in the sample to the total number of plants in the sample:

$\text{Sample Proportion} = \frac{50}{91}$

Let's calculate that:

$\text{Sample Proportion} = \frac{50}{91} \approx 0.549$

Rounded to two decimal places, the sample proportion is 0.55.

Final Answer:

(a) Population proportion: 0.62

(b) Sample proportion: 0.55

---

Would you like further details on any part of the calculation?

Here are 5 related questions for practice:

1. What is the difference between population and sample proportion?
2. How does increasing the sample size affect the sample proportion?
3. If the sample had 60 cacti out of 91 plants, what would be the new sample proportion?
4. How would you interpret a sample proportion much higher than the population proportion?
5. Why is it important to round to two decimal places in statistical analysis?

Tip: When working with proportions, always ensure your fractions are simplified and rounded consistently, especially for large datasets.