STATS CH 7 & 8

True of False: The standard deviation of the sampling distribution of the sample mean is equal to σ

FALSE

We use a calculated sample _____ to make inferences about an unknown population _____.

Statistic, Parameter

True or False: The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n>=30)

TRUE

True or False: The students t distribution assumes the population is normally distributed

TRUE

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

smaller sample size

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

stratified random sampling

As a general guideline, the normal distribution approximation can be used to describe the sampling distribution of the sample mean when

n is > or = 30

A population consists of all items of interest in a statistical

...

_________ is the value of the point estimator derived from a given sample.

A point estimate

Refers to a tendency of a sample statistic to systematically over or under estimate a population parameter

Bias

________ provides a range of values for the population parameter

Interval estimator

________ provides a single value for the population parameter

Point estimator

True or False: The width of a confidence interval estimate for a population proportion will be narrower for 90% confidence than for 95% confidence (larger sample, smaller interval)

True

_________ of x̅ is smaller than the variance of the individual observation. This is an intuitive result, suggesting that averages have less variation than individual observations.

Variance

In a statistical problem, a population consists of

all items of interest

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

approaches a normal distribution

The standard error of the sample mean is not affected by the

confidence level

An estimator is _________ if it approaches the population parameter of interest as the sample size increases.

consistent

A population parameter is a ____ even though its value may be unknown

constant

An estimator is deemed _______ if its variability between samples is smaller than that of other unbiased estimators.

efficient

A population consists of all items of interest in a statistical problem, whereas a _______ is a subset of the population

sample

The probability distribution of the sample mean is commonly referred to as the

sampling distribution of x bar

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

the parameter being estimated

measures the variability of the mean from sample to sample

the standard error of the mean

An estimator is _________ if, based on repeated sampling from the population, the average value of the estimator equals the population parameter.

unbiased

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

we have 99% confidence that we have selected a sample whose interval does not include the population mean.

Suppose you are constructing a confidence interval for the population mean. For a given sample size and standard deviation, the width of the confidence interval is______ for a greater confidence level.

wider

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

increases

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 ______

inferential statistics

The further a population proportion deviates from p= 0.50 the _____ the sample size required in order to satisfy a normal approximation.

larger

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

larger standard deviation

In general, the variability between sample means is _____ the variability between observations.

less than

The allowed probability that an interval estimate of a population mean will not contain μ is referred to as the

level of significance

A confidence interval is constructed by using the point estimate as a base, to which we ass and subtract the

margin of error

accounts for the variability of the estimator and the desired confidence level of the interval

margin of error

If the shape of the population from which a simple random sample is drawn is normal, then the shape of the sampling distribution of X-(X bar) is

normal

In order to construct a confidence interval for μ, the sampling distribution of the estimator x̅ must follow or approximately follow a ______ distribution.

normal

In order to derive a confidence interval for μ, the estimator x̅ must have a

normal sampling distribution

A particular value of an estimator

parameter

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

point estimator

the parameter p represents the

population proportion

The mean SAT score for Division 1 student-athletes is 947 with a standard deviation of 205. If you select a random sample of 60 of these students, what is the probability the mean is below 900?

.0375 HOW z= x̅ - μ/ σ / Sqrt(n) 900-947/205/Sqrt(60) = -1.78 (Use table to find answer) = .0375

38% of business students are accounting majors. A sample of 100 students is selected.What is the probability that our sample proportion will be less than .36

.34 HOW p=.38 n=100 PBAR=.36 z= PBAR-p/ Sqrt(p(1-p)/n) .36-.38/Sqrt(.38(1-.38)/100) =.3446

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

.625 (SDev/sq root of n) 10/(sqrt)256= .0625

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

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

When those responding to a survey or poll differ systematically from the non-respondents. This is an example of a

Nonresponse bias

Is a value, usually unknown (and which therefore has to be estimated), used to represent a certain population characteristic Is used to describe a population

Prameter

True or False: The students t distribution has more area in the tails than does in the normal distribution

TRUE

True or False: The students t distribution is bell shaped and symmetrical

TRUE

True or Fasle: The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means

TRUE

Desirable properties for an estimator include

unbiased-ness, efficiency, and consistency

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

simple random sample

The science that deals with the collection, classification, analysis, and interpretation of numerical facts or data. Is used to describe parameters

statistics

A statistical theory that states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

the central limit theorem

A confidence interval narrows if what is accomplished

the sample size increases the chosen confidence interval decreases

True or False: A statistic is a random variable whose value depends on the chosen random sample

true

True or False: Many different samples could be drawn from a population in order to analyze that population.

true

True or False: The central limit theorem is important in statistics because for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population

True

a random variable is also known as

a statistic

True or False: The student's t distribution is used to construct confidence intervals for the population mean when the population standard deviation is known

FALSE (UNKNOWN)

True or False: The mean of the sampling distribution of the sample mean is equal to μ

TRUE

True or False: The students t distribution approaches the normal distribution as the sample size increases

TRUE

True or False: The students t distribution has more area in the tails and less in the center than does the normal distribution

TRUE

TRUE or FALSE: Since x̅ is a random variable, its sampling distribution is simply the probability distribution derived from all possible samples of a given size from the population

True

True or False : The standard error of the mean is never larger than the standard deviation of the population

True

True or False: Cluster sampling works best when most of the variation in a population is within groups and not between groups

True

True or False: the standard error of the mean decreases as the sample size increases

True

True or False:The sample size required to approximate the normal distribution depends on how much the population varies from normality

True

Is x̅ a point estimator?

YES

When the sample is not a representative of the population we are trying to describe. This is a characteristic of ______ sample.

a bad sample

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

confidence interval

If an unbiased estimator is ______, its standard error must be lower than that of other unbiased estimators

efficient

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

estimator

when a sample is used to make inferences about a population parameter, it is referred to as an

estimator

A 95% confidence interval for the population mean implies that

for repeated samples 95% of the sample means will fall within the interval

The estimator x̅ follows a normal distribution when the underlying population follows a _____ distribution.

normal

A ________ is a descriptive measure for a qualitative variable

proportion

Sampling distributions describe the distribution of

statistics

Stratified sampling is preferred to cluster sampling when the objective is

to increase precision

True or False: A parameter is a constant although its value may be unknown

true

A particular value of the estimator is called an

estimate

True or False: The students t distribution, as the number of degrees of freedom increases, the t distribution approaches the normal distribution

TRUE

_________ of x̅ is the same as the expected value of the individual observation. In other words, if we were to sample repeatedly from a given population, in the average value of the sample means will equal the population mean from the underlying population

Expected Value

If the population from which the sample is drawn is normally distributed, then the sampling distribution of the sample mean is

always normally distributed

If a simple statistic consistently over or under estimates a population parameter then there is

bias

90% of restaurant customers order coffee with desert. If we take a sample of 144 customers who ordered desert, what is the probability that greater than .92 ordered coffee?

.2119 How PBAr= .92 n=144 p=.90 z= .92-.90 ---------- = .80 Sqrt(.9(1-.9)/144) Then use z table and .80 to get .7881 After that do this --> 1-.7881 = .2119

A manufacturer of batteries for portable hand tools wishes to investigate the length of time a battery will last between charges at a fixed load. A sample of 45 batteries had a mean length of time of 4.3 hours with a standard deviation of 0.25 hours. Construct a 95 percent confidence interval for the population mean.

4.23 to 4.37 We are 95% confident that the mean of a sample of batteries is between 4.23 and 4.37 How n= 45 x̅ = 4.3 s= .25 4.3 +- 1.96(.25/Sqrt(45)) = 4.23 to 4.37

Police Chief Aaron Ard of River City reports 500 traffic citations were issued last month. A sample of 35 of these citations showed the mean amount of the fine was $54, with a standard deviation of $4.50. Construct a 95 percent confidence interval for the mean amount of a citation in River City.

52.51 to 55.49 We are 95% confident that the mean amount of citation in River City is between 52.51 and 55.49 How n= 35 x̅ = 54 s=4.5 54+- 1.96(4.5/Sqrt(35)) =52.51 to 55.49

A range of values used to estimate an unknown population parameter

A confidence interval

When examining the possible outcome of an election, what type of confidence interval is most suitable for estimating the current support for a candidate?

Confidence interval for the population proportion

Suppose a 95% confidence interval for 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. What will result in a reduced interval width?

an increased sample size and decrease in the confidence level.