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Term: Parameter
A number that describes some characteristic of a population
Term: Statistic
Definition: A number that estimates the value of a parameter using a sample from the population
Question: What is a sampling distribution?
Answer: The distribution of values taken by a statistic in all possible samples of the same size from the same population
Question: What is the mean of the sampling distribution of a sample proportion?
Answer: μp̂ = p (where p is the population proportion)
Question: What is the standard deviation of the sampling distribution of a sample proportion?
Answer: σp̂ = √((p(1-p))/n) (where n is the sample size)
Question: What conditions must be met to use the formula for σp̂?
Answer: 10% condition: n ≤ (.10)N (sample size is no more than 10% of the population size)
Term: Central Limit Theorem (CLT)
Definition: For a large sample size, the sampling distribution of the sample mean is approximately Normal, regardless of the shape of the population distribution
Question: What is the mean of the sampling distribution of a sample mean?
Answer: μx̄ = μ (where μ is the population mean)
Question: What is the standard deviation of the sampling distribution of a sample mean?
Answer: σx̄ = σ/√n (where σ is the population standard deviation and n is the sample size)
Question: When can you use a Normal distribution to calculate probabilities involving sample means?
Answer: When the population distribution is Normal or the sample size is large (n ≥ 30)
Question: What is the purpose of a sampling distribution?
Answer: To make inferences about a population based on a sample
Question: What is a point estimate?
Answer: Single best guess for the value of a population parameter
Question: What is the effect of increasing the sample size on the variability of the sampling distribution?
Answer: Increasing the sample size decreases the variability
Question: What is the difference between a statistic and a parameter?
Answer: A parameter describes the population, while a statistic describes a sample
Question: What is the 10% condition and why is it important?
Answer: When sampling without replacement, the sample size n should be less than 10% of the population size N (n ≤ 0.10N) to use the standard deviation formula for sample proportions
