Statistics Ch.6-8

It is symmetric around its mean

A characteristic of the normal distribution is that?

Range of values used to estimate an unknown population parameter

A confidence interval can be interpreted as a ?

Normal Curve/Bell Curve

A graph depicting the normal probability density function is often referred to as this

100

A population has a mean of 100 and a standard deviation of 10. A random sample of 25 is selected. The expected value of x̅ is equal to

Has slightly broader tails than the z distribution

A t distribution

Standard Deviation

Calculated as the positive square root of the variance

Sample

subset of a population

Estimate

A particular value of the estimator

Simple Random Sample

A sample of n observations which has the same probability of being selected from the population as any other sample of n observations

When most of the variation in a population is within groups and not between groups

Cluster sampling works best ?

A consistent estimator approaches the estimated population parameter as the sample size grows larger. population parameter.

How is the consistency of an estimator defined?

The population mean

If we were to sample repeatedly from a given population, the average value of the sample means will equal

Expected Value

If we were to sample repeatedly from a given population, the average value of the sample means will equal the population mean from the underlying population

Stratified random sampling

In ?, the population is divided up into mutually exclusive and collectively exhaustive groups called strata. The sample consists of elements from each stratum

All items of interest

In a statistical problem, a population consists of ?

Less than

In general, the variability between sample means is ? the variability between observations

Those responding to a survey or poll differ systematically from the non-respondents

Nonresponse bias occurs when ?

Confidence Interval

Provides a range of values, that with a certain level of confidence, contains the population parameter of interest

Inferential Statistics

The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is BEST referred to as ?

Approaches a normal distribution

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sampling proportion ?

Population

consists of all items in a statistical problem

Higher confidence level

Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the interval is wider, for a ?

Population Proportion

The parameter p represents the ?

Sampling Distribution

The probability distribution derived from all possible samples of a given size from the population

0.50

The probability that a normal random variable X is less than its mean is equal to?

Bell Shaped

The shape of the graph depicting the normal probability density function is?

Confidence level and Sample size

When constructing a confidence interval for the population mean, the factors that affect the width of the confidence interval for a given standard deviation are ?

Widens

When the confidence level increases from 95% to 99%, the confidence interval for the population mean ?

Normal distribution

When the sample size is sufficiently large, we can approximate the sampling distribution of the sample proportion using the ?

The number of states in the USA

All of the following are examples of random variables that likely follow a normal distribution EXCEPT?

Estimator

When a statistic is used to estimate a parameter, it is referred to as an ________

0.50

The area under a normal curve below its expected value is ______ ?

compute x values for given probabilities

The inverse transformation is used to?

Zero

The mean of the standard normal distribution is equal to ____ ?

Symmetric

The mean, median, and mode are all equal for a normally distributed random variable

Mean and Variance

The normal distribution is completely described by these two parameters?

Completely Described by Two Parameters

The population mean and the population variance. The population mean describes the central location and the population variance describes the dispersion of the distribution

0.625

A population has a mean of 50 and a standard deviation of 10. A random sample of 256 is selected. The standard error of x̅ is equal to

Central limit theorem

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of the sample mean whenever the sample size is large is known as the ?

Sample Statistic

We use a calculated _____ to make inferences about the unknown population parameter

Parameter

We use a sample statistic to make inferences about an unknown population ?

Variance

An intuitive result, suggesting that averages have less variation than individual observations

2.5%

An investment strategy has an expected return of 12 percent and a deviation of 10 percent. If investment returns are normally distributed, the probability of earning a return of more than 32 percent is CLOSEST to?

5% of the sample means will fall outside of the corresponding confidence interval

For a 95% confidence interval for the population mean, if sample of size n are drawn repeatedly from a given population, then ?

68%

For data that are normally distributed, the percentage of the data that falls within one standard deviation of the mean is

Empirical Rule

Gives the approximate percentage of values that fall within 1, 2, or 3 standard deviations of the mean. Approximate percentages are appropriate for many real world applications where the normal distribution is used only as an approximation. For normally distributed random variables, these percentages are exact

An interval estimator provides a range of values for the population parameter whereas a point estimator provides a single value

How does an interval estimator differ from a point estimator?

Bias

If a sample statistic consistently over - or under - estimates a population parameter, then there is ?

Unbiased estimator

If the expected value of an estimator is equal to the unknown parameter being estimated, then the estimator is BEST characterized as a(n)

Stratified Versus Cluster Sampling

In stratified sampling, the sample consists of elements from each group, whereas in cluster sampling, the sample consists of elements from the selected groups. Stratified sampling is preferred when the objective is to increase precision and cluster sampling is preferred when the objective is to reduce costs

The Inverse Transformation

So far we have used the normal transformation to compute probabilities for given x values. We can use the inverse transformation to compute x values for given probabilities

The positive square root of the variance of x̅

The standard deviation of x̅ is calculated as ?

Confidence level

The standard error of the sample mean is NOT affected by the ?

Point Estimate and the Margin of Error

The two main components of a confidence interval are the ?

Point Estimate

The value of the point estimator derived from a given sample

The probability that Z is less than or equal to a given z value

The z table provides the cumulative probabilities for a given z. What does 'cumulative probabilities' mean?

True

True of False: Many different sampling could be drawn from a population in order to analyze that population

True

True or False: A point estimator is a function of a random sample used to make inferences about the value of an unknown population parameter

The Normal Transformation

We transform X into Z by subtracting from X its mean and dividing by its standard deviation

It is representative of the population we are trying to decide

What is a primary requirement for a "good" sample?

Desired level of confidence

Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x and the ?

Proportion

Which of the following is a descriptive measure for a qualitative variable?

x̅ = 20

Which of the following is considered an estimate ?

A parameter is a constant although its value may be unknown

Which of the following statements is MOST accurate?

Increase precision

Stratified sampling is preferred to cluster sampling when the objective is ?

Point Estimators

A function of the random sample used to make inferences about the value of an unknown population parameter

Unbiasedness, efficiency, and consistency

Desirable properties for an estimator include

- Heights and weights of newborn babies - Scores on the SAT - Cumulative debt of college graduates

Examples of random variables that closely follow a normal distribution include:

Selection Bias

Refers to a systematic exclusion of groups from consideration for the sample

p

Represents the proportion of success in the population, where success is defined by a particular outcome

Equal to 0.5

Due to symmetry, the probability that the standard normal random Z is greater than 0 is?

Margin of Error

A confidence interval is generally associated with a ________ that accounts for the variability of the estimator and the desired confidence level of the interval

Consistency

A desirable property, which is often considered a minimum requirement for an estimator; An estimator is consistent if it approaches the population parameter of interest as the sample size increases

Bias

A primary requisite for a "good" sample is that it be representative of the population we are trying to describe. When the information from a sample is not typical of information in the population in a systematic way, we say that _____ bias has occurred

Standard Normal Distribution

A special case of the normal distribution with a mean equal to zero and a standard deviation (or variance) equal to one

Increases

An estimator is consistent if approaches the population parameter of interest as the sample size

The parameter being estimated

An estimator is unbiased if the average value of the estimator is equal to ?

Unbiased

Based on repeated sampling from the population, the average value of the estimator equals the population parameter