Math Problem Statement
Solution
To solve this problem, we need to find both the sample proportion and the population proportion of attendees who were children at the Gazelles' match. Let's go through each part:
Given Information:
- Population Proportion: Out of every 56 attendees at the match, 25 were children.
- Sample Proportion: In a sample taken by the facilities manager, 43 out of 89 attendees were children.
Solution:
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(a) Sample Proportion (p-hat): Calculating this: So, the sample proportion (rounded to two decimal places) is 0.48.
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(b) Population Proportion (p): Calculating this: So, the population proportion (rounded to two decimal places) is 0.45.
Answer:
- (a) Sample Proportion:
- (b) Population Proportion:
Would you like further explanation on any step or more details?
Follow-up Questions:
- How does the sample proportion differ from the population proportion?
- Why do we use different symbols ( and ) for sample and population proportions?
- What would be the effect of a larger sample size on the accuracy of in estimating ?
- How would we calculate a confidence interval for this sample proportion?
- In what situations might the sample proportion differ significantly from the population proportion?
Tip:
Always ensure to label sample and population proportions correctly, as they represent data from different groups and serve different purposes in statistical analysis.
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Math Problem Analysis
Mathematical Concepts
Statistics
Proportion
Sample Proportion
Population Proportion
Formulas
Sample Proportion (p̂) = (Number of children in sample) / (Total sample size)
Population Proportion (p) = (Number of children in population) / (Total population size)
Theorems
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Suitable Grade Level
Grades 9-10
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