P-Hat Calculator
Calculate sample proportion (p̂) from the number of occurrences and sample size
Calculate Sample Proportion (p̂)
Number of successful outcomes or events of interest
Total number of observations in the sample
Sample size (n) must be greater than 0
Sample Proportion Results
Example Calculation
School Menu Poll Example
Scenario: A poll about adding carrot pumpkin soup to the school menu
Sample size (n): 700 students
Favorable responses (x): 450 students said "yes"
Calculation: p̂ = 450 / 700 = 0.6429
Result: 64.29% of students favor adding the soup to the menu
Political Poll Example
Scenario: Polling voter preference for a candidate
Sample size (n): 1,200 voters
Supporters (x): 720 voters
Calculation: p̂ = 720 / 1,200 = 0.6000
Result: 60% of polled voters support the candidate
Key Concepts
Sample Proportion
Ratio of successes to sample size
Ranges from 0 to 1
Percentage Form
p̂ × 100 for easier interpretation
Common in polls and surveys
Complement
Proportion without the characteristic
q̂ = 1 - p̂
Formula Reference
p̂: Sample proportion (p-hat)
x: Number of occurrences/successes
n: Total sample size
Range: 0 ≤ p̂ ≤ 1
Common Applications
Opinion polls and surveys
Clinical trial success rates
Market research studies
Quality control testing
Election polling
Understanding Sample Proportion (p̂)
What is P-Hat?
The sample proportion, denoted as p̂ (pronounced "p-hat"), represents the ratio of the number of occurrences of a particular event to the total sample size. It's a fundamental statistic in inferential statistics used to estimate the true population proportion.
Key Characteristics
- •Always between 0 and 1 (inclusive)
- •Subject to sampling variability
- •Estimates the population proportion
- •Commonly expressed as percentage
Formula Breakdown
p̂ = x / n
p̂: Sample proportion (the result)
x: Number of favorable outcomes or occurrences
n: Total sample size
Important: The sample proportion is an estimate of the true population proportion and may vary between different samples from the same population.
Sample vs Population Proportion
Sample Proportion (p̂)
Calculated from a sample of the population. Used to estimate the population proportion.
Example: 60% of 1,000 surveyed voters support a candidate
Population Proportion (p)
The true proportion in the entire population. Usually unknown and estimated using p̂.
Example: The actual percentage of all voters who support the candidate
Practical Applications
📊 Market Research
Determine what percentage of customers prefer a product feature
🏥 Medical Studies
Calculate treatment success rates in clinical trials
🗳️ Political Polling
Estimate voter support for candidates or policies