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
