Statistics and Probability Chapter 6 Flashcards

Questions and Answers

What is a statistic?

A number that describes some characteristic of a sample (correct)

A number that describes some characteristic of a population

The distribution of values taken by a statistic in all possible samples

None of the above

What distinguishes a parameter from a statistic?

A parameter is always a larger number

A parameter describes a population (correct)

A parameter describes a sample

A parameter can never be estimated

What is a sampling distribution?

The distribution of a statistic based on one sample

The distribution of values taken by a statistic in all possible samples of the same size (correct)

The average value from all samples

None of the above

What defines an unbiased estimator?

Its sampling distribution mean equals the parameter being estimated Signup and view all the answers

What does the Large Counts condition state?

The distribution of X and the distribution of p̂ will be approximately normal when np ≥ 10 and n(1 − p) ≥ 10. Signup and view all the answers

What is the Central Limit Theorem (CLT)?

When n is large, the sampling distribution of the sample mean x̅ is approximately normal regardless of the population distribution. Signup and view all the answers

The Normal/Large Sample condition only applies when the sample size is large (n ≥ 30).

True Signup and view all the answers

What describes the sampling distribution of the sample proportion p̂?

The distribution of values taken by the sample proportion p̂ in all possible samples of the same size Signup and view all the answers

What is the primary purpose of the sampling distribution of the sample mean x̅?

To analyze the distribution of means from samples of the same size Signup and view all the answers

Study Notes

Key Concepts in Statistics

Statistic: Represents a characteristic of a sample, offering insights into data points drawn from a specific subset of a larger population.
Parameter: Describes a characteristic of the entire population, essential for understanding the overall data landscape.
Sampling Distribution: The range of values a statistic can take across all potential samples of a fixed size from a population.

Estimation and Sampling

Unbiased Estimator: A statistic that correctly estimates a parameter if its sampling distribution's mean coincides with the parameter value being estimated.
Sampling Distribution of the Sample Count (X): The distribution reflects the sample count across all possible samples of identical size from the same population.
Sampling Distribution of the Sample Proportion (p̂): Describes the distribution of sample proportions from all samples of the same size, providing insights on population proportions.
Sampling Distribution of the Sample Mean (x̅): A conceptual framework depicting the variations of sample means from different samples of the same size.

Conditions for Normal Approximation

Large Counts Condition: Ensures the sampling distributions of successes are approximately normal. It requires np ≥ 10 and n(1 − p) ≥ 10. For chi-square tests, expected counts should be a minimum of 5.
Central Limit Theorem (CLT): States that the sampling distribution of the sample mean approximates a normal distribution when the sample size is sufficiently large (n is large) regardless of the population's original distribution.
Normal/Large Sample Condition: Necessary for inference about a mean; demands that either the population is normally distributed or the sample size is large (n ≥ 30). Small samples must exhibit no significant skewness or outliers. Confirmation of this condition is crucial for comparisons between two means.

Description

Explore key terms from Chapter 6 of Starnes' Statistics and Probability with Applications. This quiz will help reinforce your understanding of important concepts like statistics, parameters, and sampling distributions. Perfect for students looking to ace their statistics course.