Statistics 122 Module 9 Flashcards

Questions and Answers

A continuity correction is made to a discrete whole number, such as x, in the binomial distribution. Which of the following intervals would we use to represent x?

x - 0.5 to x + 0.5

Which of the following is NOT a conclusion of the Central Limit Theorem?

The distribution of the sample data will approach a normal distribution as the sample size increases.

The population standard deviation is irrelevant. (correct)

Sample means will be normally distributed regardless of sample size.

The mean of the sampling distribution will equal the population mean.

Which of the following is NOT a property of the sampling distribution of the variance?

The mean of the sampling distribution of the variance is the population variance.

The variance of the sampling distribution is equal to the population variance.

It is biased.

The distribution of sample variances tends to be a normal distribution. (correct)

Which statement below indicates the area to the left of 19.5 before a continuity correction is used?

At most 19 Signup and view all the answers

Why must a continuity correction be used when using the normal approximation for the binomial distribution?

The normal distribution is a continuous probability distribution being used as an approximation to the binomial distribution, which is a discrete probability distribution. Signup and view all the answers

Which of the following is NOT a requirement for using the normal distribution as an approximation to the binomial distribution?

The sample is the result of conducting several dependent trials of an experiment in which the probability of success is p. Signup and view all the answers

Which of the following is a biased estimator? That is, which of the following does not target the population parameter?

Median Signup and view all the answers

The Rare Event Rule for Inferential Statistics states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), then we conclude __________.

the assumption is probably not correct Signup and view all the answers

Which of the following is NOT a property of the sampling distribution of the sample mean?

The distribution of the sample mean tends to be skewed to the right or left. Signup and view all the answers

Study Notes

Continuity Correction

A continuity correction adjusts discrete values in the binomial distribution by using intervals of x - 0.5 to x + 0.5 to improve the approximation with normal distribution.

Central Limit Theorem

The Central Limit Theorem asserts that the distribution of sample means will approach a normal distribution as the sample size increases.

Sampling Distribution of Variance

The sampling distribution of variance does not follow a normal distribution; it tends to be positively skewed, especially in small samples.

Areas in Continuous Distribution

To represent the area to the left of 19.5 before applying a continuity correction, one would consider "at most 19," focusing on whole numbers.

Importance of Continuity Correction

Continuity correction is necessary when using normal approximation for the binomial distribution since binomial data is discrete while normal distribution is continuous.

Normal Approximation Requirements

A normal distribution can be used to approximate a binomial distribution when the trials are independent and not dependent on each other (not the result of dependent trials).

Biased Estimators

The median is considered a biased estimator because it does not target the population parameter accurately compared to other estimators like the mean.

Rare Event Rule

According to the Rare Event Rule for Inferential Statistics, if an observed event's probability is extremely low (less than 0.05), it suggests that the initial assumption is likely incorrect.

Properties of Sample Mean Distribution

The sampling distribution of the sample mean should be normally distributed regardless of the population distribution, contradicting the idea that it can be skewed.

Description

Test your knowledge with these flashcards covering key concepts from Statistics 122, Module 9. This includes topics such as the continuity correction in binomial distributions and the Central Limit Theorem. Perfect for students looking to reinforce their understanding of statistical theory.