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What is the definition of random variation?
Data values scattered without a discernible pattern, often seen in random samples.
What is the definition of non-random variation?
Indicates an underlying pattern or structure in the data, resulting from measurement error, bias or systematic differences.
What is the definition of a normal curve?
A symmetrical, bell-shaped curve used extensively in statistical inference.
What is the Large Counts Condition?
Both expected successes ($np$) and expected failures ($n(1-p)$) must be at least 10.
What is a Z-score?
A measure of how many standard deviations a data point is from the mean.
Explain the concept of random variation.
Data points are scattered with no discernible pattern, indicating pure chance.
Explain the importance of the normal curve in statistical inference.
It allows us to calculate probabilities in sampling distributions and standardize data using z-scores.
Explain the meaning of 'normal' in statistics.
Refers to a specific bell-shaped curve, not necessarily 'typical' or 'average'.
Explain the purpose of checking the Large Counts Condition.
To ensure that the sampling distribution is approximately normal, allowing for valid statistical inference.
Explain how z-scores are used with the normal curve.
Z-scores standardize sample data, allowing us to use the normal curve to determine probabilities.
What is the formula to check for large counts condition (successes)?
$np \ge 10$, where $n$ = sample size and $p$ = probability of success.
What is the formula to check for large counts condition (failures)?
$n(1-p) \ge 10$, where $n$ = sample size and $p$ = probability of success.
What is the formula for calculating the z-score?
$z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$
What is the formula for calculating the sample proportion?
$\hat{p} = \frac{x}{n}$ where $x$ is the number of successes and $n$ is the sample size.