Statistics Test 3 Flashcards

Questions and Answers

The normal curve is symmetric about its mean, μ.

True

The area under the normal curve to the right of μ equals ______.

1/2

The points at x=_ and x=_ are the inflection points on the normal curve.

μ−σ, μ+σ

Could the graph represent a normal density function if it is a bell curve?

True Signup and view all the answers

Could the graph represent a normal density function if it is skewed right?

False Signup and view all the answers

The histogram is bell-shaped, indicating that a normal distribution could be used as a model for the variable.

True Signup and view all the answers

Yes, the histogram has the shape of a normal curve, suggesting a normal distribution could be used.

True Signup and view all the answers

The notation zα is the z-score that the area under the standard normal curve to the right of zα is ______.

α Signup and view all the answers

The sampling distribution of x has mean μx= and standard deviation σx=.

μ, σ/sqrtn Signup and view all the answers

The standard deviation of the sampling distribution of x, denoted σx, is called the _ of the .

standard, error, mean Signup and view all the answers

The distribution of the sample mean, x, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of sample size.

True Signup and view all the answers

Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?

No, because of the Central Limit Theorem. Signup and view all the answers

The _____ , denoted p, is given by the formula p= where x is the number of individuals with a specified characteristic in a sample of n individuals.

Sample, Proportion, x/n Signup and view all the answers

True or False: The population proportion and sample proportion always have the same value.

False Signup and view all the answers

The mean of the sampling distribution of p hat is p.

True Signup and view all the answers

A is the value of a statistic that estimates the value of a parameter.

point estimate Signup and view all the answers

The _ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted _.

level of confidence, (1-alpha) * 100% Signup and view all the answers

To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.

False Signup and view all the answers

Provide two recommendations for decreasing the margin of error of the interval.

Increase the sample size, Decrease the confidence level. Signup and view all the answers

How does the decrease in confidence affect the sample size required?

Decreasing the confidence level decreases the sample size needed. Signup and view all the answers

What effect does doubling the required accuracy have on the sample size?

Doubling the required accuracy nearly quadruples the sample size. Signup and view all the answers

How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable?

Increasing the level of confidence increases the sample size required. Signup and view all the answers

Explain why the t-distribution has less spread as the number of degrees of freedom increases.

The t-distribution has less spread as the degrees of freedom increase because, as n increases, s becomes closer to σ by the law of large numbers. Signup and view all the answers

True or false: The chi-square distribution is symmetric.

False Signup and view all the answers

True or false: To construct a confidence interval about a population variance or standard deviation, either the population from which the sample is drawn must be normal, or the sample size must be large.

False Signup and view all the answers

Why are the results from parts (a) and (b) so close?

The results are close because $0.52(1−0.52)=0.2496$ is very close to 0.25. Signup and view all the answers

Does the boxplot suggest that there are outliers?

False Signup and view all the answers

Verify that the requirements for constructing a confidence interval about p are satisfied.

is stated to be np(1-p) greater than or equal to sample size can be assumed to be population size. Signup and view all the answers

Study Notes

Normal Curve Characteristics

The normal curve is symmetric about its mean, μ; mean, median, and mode are equal.
Area to the right of μ under the normal curve equals 1/2.

Inflection Points

Inflection points on the normal curve are located at x = μ - σ and x = μ + σ.

Normal Density Function

A bell curve graph can represent a normal density function, while a skewed right graph cannot.

Histogram Analysis

A bell-shaped histogram indicates that a normal distribution is suitable for modeling the variable.
For phone call lengths, a bell-shaped histogram confirms the use of a normal distribution model.

Sampling Distribution

The mean of the sampling distribution, μx, equals μ, and the standard deviation, σx, equals σ/sqrt(n).
Standard deviation of the sampling distribution is called the standard error of the mean.

Distribution Normality

The sample mean will be normally distributed if the original population is normal, regardless of sample size.
According to the Central Limit Theorem, sampling distribution of x approaches normality as sample size n increases.

Proportions

Sample proportion, denoted by p, is calculated as p = x/n, where x is the number of individuals with a characteristic in the sample.
False statement: The population proportion and sample proportion always have the same value.

Confidence Intervals

The mean of the sampling distribution of p hat is equal to p.
The level of confidence quantifies the expected proportion of intervals containing the parameter.

Sample Size and Accuracy

Increasing the sample size or decreasing the confidence level lowers the margin of error in confidence intervals.
A decrease in the confidence level reduces the required sample size.

Sample Size Sensitivity

Doubling the required accuracy nearly quadruples the necessary sample size.
Increasing the confidence level requires a larger sample size for a fixed margin of error.

T-Distribution Behavior

T-distribution has less spread as the number of degrees of freedom increases, making results closer to the population standard deviation.

Chi-Square Distribution

Chi-square distribution is not symmetric; it is skewed to the right.
To construct a confidence interval for population variance or standard deviation, the sample must come from a normally distributed population.

Boxplot and Outliers

A boxplot indicates no outliers if all data points are within the 1.5(IQR) boundary.

Confidence Interval Requirements

To verify that requirements for constructing a confidence interval about p are met, the product np(1-p) must equal or exceed the sample size.

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Description

This quiz focuses on key concepts related to the normal curve in statistics. It covers the properties of the normal distribution, including symmetry, mean, median, and the area under the curve. Perfect for reviewing essential statistical concepts for exams.

Statistics Test 3 Flashcards

Questions and Answers

The normal curve is symmetric about its mean, μ.

The area under the normal curve to the right of μ equals ______.

The points at x=_______ and x=_______ are the inflection points on the normal curve.

Could the graph represent a normal density function if it is a bell curve?

Could the graph represent a normal density function if it is skewed right?

The histogram is bell-shaped, indicating that a normal distribution could be used as a model for the variable.

Yes, the histogram has the shape of a normal curve, suggesting a normal distribution could be used.

The notation zα is the z-score that the area under the standard normal curve to the right of zα is ______.

The sampling distribution of x has mean μx=______ and standard deviation σx=______.

The standard deviation of the sampling distribution of x, denoted σx, is called the _____ ____ of the ____.

The distribution of the sample mean, x, will be normally distributed if the sample is obtained from a population that is normally distributed, regardless of sample size.

Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why?

The _____ , denoted p, is given by the formula p= where x is the number of individuals with a specified characteristic in a sample of n individuals.

True or False: The population proportion and sample proportion always have the same value.

The mean of the sampling distribution of p hat is p.

A ________ ________ is the value of a statistic that estimates the value of a parameter.

The _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted _______.

To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.

Provide two recommendations for decreasing the margin of error of the interval.

How does the decrease in confidence affect the sample size required?

What effect does doubling the required accuracy have on the sample size?

How does increasing the level of confidence in the estimate affect sample size? Why is this reasonable?

Explain why the t-distribution has less spread as the number of degrees of freedom increases.

True or false: The chi-square distribution is symmetric.

True or false: To construct a confidence interval about a population variance or standard deviation, either the population from which the sample is drawn must be normal, or the sample size must be large.

Why are the results from parts (a) and (b) so close?

Does the boxplot suggest that there are outliers?

Verify that the requirements for constructing a confidence interval about p are satisfied.

Study Notes

Normal Curve Characteristics

Inflection Points

Normal Density Function

Histogram Analysis

Sampling Distribution

Distribution Normality

Proportions

Confidence Intervals

Sample Size and Accuracy

Sample Size Sensitivity

T-Distribution Behavior

Chi-Square Distribution

Boxplot and Outliers

Confidence Interval Requirements

Studying That Suits You

Description

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Normal Curve Flashcards

The points at x=_ and x=_ are the inflection points on the normal curve.

The sampling distribution of x has mean μx= and standard deviation σx=.

The standard deviation of the sampling distribution of x, denoted σx, is called the _ of the .

A is the value of a statistic that estimates the value of a parameter.

The _ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. It is denoted _.