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What are the differences between the sampling distribution of proportions and the sampling distribution of means?
Sampling Distribution of Proportions: Deals with categorical data, uses sample proportions, and checks the large counts condition. | Sampling Distribution of Means: Deals with numerical data, uses sample means, and relies on the Central Limit Theorem or a normally distributed population.
What are the key differences between one-sample and two-sample scenarios when dealing with sampling distributions?
One-Sample: Involves making inferences about a single population. | Two-Sample: Involves comparing two populations and requires checking conditions for both samples.
What is the difference between the standard deviation of a population and the standard deviation of a sampling distribution?
Population Standard Deviation: Measures the variability within the entire population. | Standard Deviation of Sampling Distribution: Measures the variability of sample statistics (like means or proportions) across different samples.
What is the difference between the Large Counts condition and the Central Limit Theorem?
Large Counts: Used for sample proportions, requires at least 10 expected successes and failures. | Central Limit Theorem: Used for sample means, states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (n โฅ 30).
What are the differences between the conditions for proportions and means?
Conditions for Proportions: Random, Independence (10% condition), Normality (Large Counts condition). | Conditions for Means: Random, Independence (10% condition), Normality (Population is normal or n โฅ 30).
What is the formula for the standard deviation of the sampling distribution of proportions?
$\sqrt{\frac{p(1-p)}{n}}$, where p is the population proportion and n is the sample size.
What is the formula for the standard deviation of the sampling distribution of means?
$\frac{\sigma}{\sqrt{n}}$, where ฯ is the population standard deviation and n is the sample size.
What is the Large Counts Condition Formula?
$np \geq 10$ and $n(1-p) \geq 10$
What is the formula for the standard deviation of the sampling distribution of the difference in proportions?
$\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$
What is the formula for the standard deviation of the sampling distribution of the difference in means?
$\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$
What is the definition of a sampling distribution?
A distribution of a statistic (like a sample mean or sample proportion) from all possible samples of the same size from a population.
What is the sampling distribution of proportions?
The distribution of sample proportions calculated from multiple random samples of the same size taken from a population.
What is the sampling distribution of means?
The distribution of sample means calculated from multiple random samples of the same size taken from a population.
Define the Central Limit Theorem (CLT).
A theorem stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution.
What is the 10% condition?
When sampling without replacement, verify that the sample size is no more than 10% of the population size to ensure independence.