Math Problem Statement
Solution
To solve this problem, let’s break it down into two parts:
Given Data:
- Population: 960 products.
- Number of Rainbow Lollipops in the Population: 290.
- Sample Size: 60 products.
- Number of Rainbow Lollipops in the Sample: 14.
Solution:
(a) Population Proportion
The population proportion () is the ratio of rainbow lollipops in the entire population: Calculating this:
(b) Sample Proportion
The sample proportion () is the ratio of rainbow lollipops in the sample: Calculating this:
Answers:
- (a) Population proportion () = 0.30
- (b) Sample proportion () = 0.23
Would you like further details on this solution or have any questions?
Related Questions:
- How is a sample proportion different from a population proportion?
- Why do we round proportions to two decimal places in statistics?
- What impact does sample size have on the accuracy of a sample proportion?
- How can we determine if the sample is representative of the population?
- What statistical methods could verify the accuracy of the sample's proportion?
Tip:
Always differentiate between sample and population notations: population proportion is , while sample proportion is .
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Math Problem Analysis
Mathematical Concepts
Statistics
Proportion Calculation
Population vs. Sample Proportion
Formulas
p = (Number of Rainbow Lollipops in Population) / (Total Population Size)
p̂ = (Number of Rainbow Lollipops in Sample) / (Sample Size)
Theorems
Law of Large Numbers
Suitable Grade Level
Grades 10-12
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