Question
The Plush Zoo store sells stuffed animals. The store is running a special on teddy bears this month. One day, the shopkeeper took a sample of stuffed animals at the store. She found that 5 of the 31 stuffed animals that she sampled were teddy bears. The store had 780 stuffed animals on that day, and 120 of those stuffed animals were teddy bears. For the shopkeeper's sample, find and write with proper notation the sample proportion and population proportion of stuffed animals that were teddy bears. Write the proportions as decimals (not percentages) rounded to two decimal places. (a) Sample proportion: (Choose one) \( \mathbf{V}= \) (b) Population proportion: (Choose one) \( \mathbf{V} \)
Ask by Conner Li. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) Sample proportion: \( \hat{p} = 0.16 \)
(b) Population proportion: \( p = 0.15 \)
Solution
**Step 1: Compute the Sample Proportion**
The sample proportion, denoted by \( \hat{p} \), is calculated as:
\[
\hat{p} = \frac{\text{Number of teddy bears in the sample}}{\text{Total sample size}} = \frac{5}{31} \approx 0.16
\]
**Step 2: Compute the Population Proportion**
The population proportion, denoted by \( p \), is calculated as:
\[
p = \frac{\text{Number of teddy bears in the population}}{\text{Total number in the population}} = \frac{120}{780} \approx 0.15
\]
**Final Answers:**
(a) Sample proportion: \( \hat{p} \approx 0.16 \)
(b) Population proportion: \( p \approx 0.15 \)
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Simplify this solution Beyond the Answer
To find the sample proportion of stuffed animals that were teddy bears, we take the number of teddy bears in the sample and divide it by the total number of stuffed animals in the sample. Thus, we have: \[ \text{Sample proportion} = \frac{5}{31} \approx 0.16 \] Now for the population proportion, we take the total number of teddy bears in the store and divide it by the total number of stuffed animals in the store. So, we get: \[ \text{Population proportion} = \frac{120}{780} \approx 0.15 \] Therefore, (a) Sample proportion: \( \mathbf{0.16} \) (b) Population proportion: \( \mathbf{0.15} \)
