Business Stats Test 3

X be normally distributed

in order to derive a confidence interval of mu, it is essential that....

confidence interval

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

z table

provides cumulative probabilities for a given z

selection bias

refers to a systematic exclusion of certain groups from consideration for the sample

parameter p

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

statistics

sampling distributions describe the distribution of

variability of the estimator

since numerous samples of size n can be drawn from the underlying population, the ______________ is captured by its standard deviation, or its standard error

family of distributions identified by the df parameter

since the tdf distribution is a ____________________________ the t table is not as comprehensive as the z table; it only lists probabilities corresponding to a limited number of values

variance of X

smaller than the variance of the individual observation; this is an intuitive result, suggesting that averages have less variation than individual observations

sampling distribution

the probability distribution of the sample mean X; since X is a random variable, its sampling distribution is simply the probability distribution derived from all possible samples of a given size from the population

expected value of X

the same as the expected value of the individual observation; 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 sampling

the sample consists of elements from each group; preferred when the objective is to increase precision

consistency

another desirable property which is often considered a minimum requirement for an estimator

approximate percentages

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

approximately normal whenever the sample size is sufficiently large (n > 30), generated by repeatedly taking samples of size n and computing the sample means, and the mean of the sampling distribution of the sample mean is equal to mu

the sampling distribution of the sample mean....

the standard deviation of the sampling distribution of the sample mean is NOT equal to funky o

the sampling distribution of the sample mean:

is never larger than the standard deviation of the population, decreases as the sample size increases, and measures the variability of the mean from sample to sample

the standard error of the mean

point estimate

the value of the point estimator derived from a given sample

narrower for 90% confidence than for 95% confidence

the width of a confidence interval estimate for a proportion will be

does not contain mu

this is the allowed probability that the estimation procedure will generate an interval that....

random variable X

this represents a certain characteristic of a population under study

desirable properties of a point estimator:

1) unbiased-ness 2) consistency 3) efficiency

important feature of the sampling distribution of the sample mean X

irrespective of the sample size "n", X is normally distributed if the population X from which the sample is drawn is normal; in other words.... if X is normal with expected value "mu" and standard deviation "funky o", then X is also normal with expected value "mu" and standard deviation "funky o/square root of n"

primary requisite for a "good" sample:

it be representative of the population we are trying to describe

normal distribution

it is required that X follows a ______________ in estimating the population mean

tdf

like the z distribution, this distribution is bell-shaped and symmetric around 0 with asymptotic tails

z table

lists z values along with the corresponding cumulative probabilities

symmetry

noncumulative probabilities can be evaluated using this

the population mean and the population variance

normal distribution is completely described by these two parameters

standard deviation of X

calculated as the positive square root of the variance

parameter of interest

describes a population that is qualitative rather than quantitative

population mean

describes the central location

population variance

describes the dispersion of the distribution

approximately normal if the sample size "n" is sufficiently large

for any population X with expected value mu and standard deviation "o", the sampling distribution X will be.....

approximately normal if the sample size n is sufficiently large

for any population proportion p, the sampling distribution of P is....

Yellow note:

given the symmetry of the normal distribution and the fact that the area under the entire curve is one, other probabilities can be easily computed; we can also use the table to compute z values for given cumulative probabilities

empirical rule

gives the approximate percentage of values that fall within 1, 2, or 3 standard deviations of the mean

t distribution

has slightly broader tails than the z distribution

examples of random variables that closely follow a normal distribution

heights and weights of newborn babies, scores on the SAT, and cumulative debt of college graduates

increase the sample size and decrease the confidence interval

suppose a 95% confidence interval for mu turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of population

the central limit theorem is important in statistics because

probability of error/ level of significance

the greek letter a denotes this

symmetric normal distribution

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

n greater than or equal to 30

the normal distribution approximation is justified when

np is greater than or equal to 5 and n(1-p) is greater than or equal to 5

the normal distribution approximation is justified when

quantitative

the population mean mu and population variance o2 describes __________ data

qualitative

the population proportion p is the essential descriptive measure when the data type is __________

cluster sampling

the sample consists of elements from the selected groups; preferred when the objective is to reduce costs

point estimator

the sample mean is a ___________ of the population mean and the sample proportion is a ____________ of the population proportion

binomial distriubtion

the sampling distribution of P is based on this and we can approximate it by a normal distribution for large samples, according to the central limit theorem

it has more area in the tails and less in the center than does the normal distribution, it is bellshaped and symmetrical, and as the number of degrees of freedom increases, the t distribution approaches the normal distribution

the student's t distribution

assumes the population is normally distributed, approaches the normal distribution as the sample size increases, and has more area in the tails than does the normal distribution

the t distribution....

t table

unlike the cumulative probabilities in the z table, the _______ provides the probabilities in the upper-tail of the distribution

degrees of freedom (df)

each t distribution is identified by this

confidence coefficient

(1-a)

expected value

The ___________________ of the sample means is equal to the population mean irrespective of the sample size

population parameter

is constant even though its value may be unknown

unbiased

an estimator is ___________ if, based on repeated sampling from the population, the average value of the estimator equals the population parameter

increases

an estimator is consistent if it approaches the population parameter of interest as the sample size ______________

smaller

an estimator is deemed efficient if its variability between samples is _________ than that of other unbiased estimators

point estimators

X and P are ___________ of their population counterparts mu and p; each of them provides a single value or point as an estimate of the unknown population parameter

unbiased estimators

X and P are the ____________________ of mu and p; this property is independent of the sample size

if all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval and we have 99% confidence that we have selected a sample whose interval does include the population mean

a 99% confidence interval estimate can be interpreted to mean that

margin of error

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

point estimator

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

normal curve/bell curve

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

inferential statistics

a major portion of statistics is concerned with this where we examine the problem of estimating population parameters or testing hypotheses about such parameters

estimate

a particular value of the estimator is called this

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

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

sample statistic

we use a calculated _____________ to make inferences about the unknown population parameter

sample proportion P

we use this as the point estimator of the population proportion p

estimator

when a stat is used to estimate a parameter, it is referred to as this

1) the sample size n or df=n-1 2) alpha

when determining the value of tadf, we need two pieces of info:

bias

when the info from a sample is not typical of info in the population in a systematic way, this has occurred

asymptotic tails

when the tails get closer and closer to the horizontal axis but never touch it