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The median is not always the 50th percentile.
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For any sample size n, the sampling distribution of "x bar" is normal if the population "x bar" from which the sample is drawn is uniformly distributed.
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Given that the probability distribution is normal, it is completely described by its mean μ > 0 and its standard deviation σ > 0.
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Like the z distribution, the t distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.
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Mean-variance analysis suggests that investments with lower average returns are also associated with higher risks.
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Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.
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The MAD is a less effective measure of variation when compared with the average deviation from the
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The arithmetic mean is the middle value of a data set.
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The letter Z is used to denote a random variable with any normal distribution.
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The t distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the t distribution is similar to the z distribution.
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The variance and standard deviation are the most widely used measures of central location.
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The coefficient of variation is a unit free measure of dispersion.
T
The continuous uniform distribution describes a random variable, defined on the interval [a, b], that has an equally likely chance of assuming values within any subinterval of [a, b] with the same length.
T
The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined.
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The probability density function of a continuous random variable can be regarded as a counterpart of the probability mass function of a discrete random variable.
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The probability density function of a normal distribution is in general characterized by being symmetric and bell-shaped.
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The standard deviation is the positive square root of the variance.
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The standard deviation of x bar equals the population standard deviation divided by the square root of the sample size, or equivalently, .
T
The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one.
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The standard normal table is also referred to as the z table.
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The t distribution has broader tails than the z distribution.
T
The terms central location or central tendency refer to the way quantitative data tend to cluster around some middle or central value.
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The variance is an average squared deviation from the mean.
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When a statistic is used to estimate a parameter, the statistic is referred to as an estimator. A particular value of the estimator is called an estimate.
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a box plot is useful when comparing similar information gathered at different places or times.
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A point estimate is a function of the random sample used to make inferences about the value of an unknown population parameter. A point estimator reflects the actual value of the point estimate derived from a given sample.
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An unbiased estimator is efficient if its standard error is higher than that of other unbiased estimators of the estimated population parameter.
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Examples of random variables that closely follow a normal distribution include the age and the class year designation of a college student.
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For any population x with expected value μ and standard deviation σ, the sampling distribution of "x bar" will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n <30.
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A parameter is a random variable, whereas a sample statistic is a constant.
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A sample consists of all items of interest in a statistical problem, whereas a population is a subset of the population. We calculate a parameter to make inferences about the unknown sample statistic.
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Chebyshev's theorem is only applicable for sample data.
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Cumulative distribution functions can only be used to compute probabilities for continuous random variables.
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For a given confidence level and sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.
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For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level .
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Just as in the case of the continuous uniform distribution, the probability density function of the normal distribution may be easily used to compute probabilities.
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The mean and standard deviation of the continuous uniform distribution are equal.
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The probability density function of a continuous uniform distribution is positive for all values between -∞ and +∞.
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We are often interested in finding the probability that a continuous random variable assumes a particular value.
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We calculate a parameter to make inferences about a statistic.
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13. The required sample size for the interval estimation of the population mean can be computed if we specify the population standard deviation σ, the value of based on the confidence level , and the desired margin of error D.
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A continuous random variable is characterized by uncountable values and can take on any value within an interval.
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A simple random sample is a sample of n observations which has the same probability of being selected from the population as any other sample of n observations.
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An estimator is consistent if it approaches the estimated population parameter as the sample size grows larger.
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An estimator is unbiased if its expected value equals the estimated population parameter.
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Approximately 60% of the observations in a data set fall below the 60th percentile
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Bias refers to the tendency of a sample statistic to systematically over- or underestimate a population parameter.
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For a given confidence level and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size n.
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For any population proportion p, the sampling distribution of will be approximately normal if the sample size n is sufficiently large. As a general guideline, the normal distribution approximation is justified when and .
T
If a random sample of size n is taken from a normal population with a finite variance, then the statistic follows the t distribution with (n - 1) degrees of freedom, df.
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If we had access to data that encompass the entire population, then the values of the parameters would be known and no statistical inference would be needed.
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If we want to find the required sample size for the interval estimation of the population proportion, and no reasonable estimate of this proportion is available, we assume the worst-case scenario under which .
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In a data set, an outlier is a large or small value regarded as an extreme value in the data set.
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In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum, which are proportional to the stratum's size.
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Nonresponse bias occurs when those responding to a survey or poll differ systematically from the nonrespondents.
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The Sharpe ratio measures the extra reward per unit of risk.
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The empirical rule is only applicable for approximately bell-shaped data.
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The geometric mean is a multiplicative average of a data set.
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A population consists of all items of interest in a statistical problem.
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A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.
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