BNAD Midterm 2

How many parameters are needed to fully describe any normal distribution?

2

A population has a mean of 50 and a standard deviation of 10. A random sample of 144 is selected. The expected value of (x bar) is equal to

50. The mean is the expected value.

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

68%

True or False: The expected value and the variance of the standard normal random variable Z are both zero.

False

This can be represented by a discrete random variable:

The number of defective light bulbs in a sample of 15

Is (x bar) a sample statistic?

Yes

For a continuous random variable x, the number of values

cannot be counted

The total area under the normal curve is...

equal to one

A continuous random variable has the uniform distribution on the interval [a,b] if its probability density function f(x)

is constant for all x between a and , and 0 otherwise

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

parameter

The population distribution of the sample mean is commonly referred to as the _______.

sampling distribution of (x bar)

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

sampling distribution of (x bar)

The variance of (x bar), which is equal to (squared root of the std. dev./n) is

smaller than the variance of the individual observation (std. dev. squared)

Nonresponse bias occurs when

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

The area under a normal curve below its expected value is...

0.50

For data that are normally distributed, the percentage of the data that falls within two standard deviations of the mean is

95%

True or False: A parameter is a numerical measure that describes a sample

False, a parameter describes a population

A continuous random variable is a...

normal random variable

For a continuous random variable, one characteristic of its probability density function f(x) is that the area under f(x) over all values of x is

equal to one

A random variable X follows the continuous uniform distribution if

it has an equally likely chance of assuming any value within a specified range

A characteristic of the normal distribution is that

it is asympotic

Cluster sampling works best when

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

A random variable depicted with a bell shaped curve is considered a...

normal random variable

True or False: if we had access to data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.

True. (if you have the data of entire population there is no need to make inferences using sample data)

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

n> 30

A simple random sample is a sample of observations that is

representative of the population from which it was chosen

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 ______.

sample distribution of (x bar)

A control chart is a plot of calculated statistics of a production process over______.

time

Stratified sampling is preferred to cluster sampling when the objective is

to increase precison

When do we use uniform distribution

when we have boundaries, a lower limit and an upper limit

Consider data that are normally distributed. In order to transform a standard normal value z into its unstandardized value x, we use the following formula:

x= (mean) + z(stan. dev.)

Consider data that are normally distributed. In order to transform a value x into it standardized value z, we use the following formula:

z = X - (the mean) all divided by the standard deviation

The probability that a continuous random variable X assumes a particular value x is

zero

Since the z table provides the cumulative probabilities for a given value of z, how can we calculate P(Z>z)?

= 1 - P(Z<z)

The sample size required to approximate the normal distribution depends on

how much the population varies from normally

The expected value of (x bar) is equal to the _____.

population mean

If X is a normally distributed random variable, then

the mean, the median, and the mode are all equal

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

the population mean

What is a characteristic of a bad sample?

the sample is not representative of the population we are trying to describe

Selection bias occurs when

there is a systematic exclusion of certain groups from consideration for the sample

Random samples of size 100 are taken from a population whose population proportion is 0.40. The expected value of the sample proportion is

0.40

Due to symmetry, the probability that the standard normal random variable Z is less than 0 is equal to

0.5

A continuous random variable is an example of what?

a normal random variable

What is an estimate?

a particular value of an estimator

What does a parameter describe?

a population

A particular value of an estimator is called a/an

estimate

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

estimator

If X is normally distributed with an expected value mu, and standard deviation, then (x bar) is normally distributed with

expected value mu, and standard deviation of (std.dev/square root of n)

The sample size required to approximate the normal distribution depends on

how much the population varies from normality

True or false: if we had to access to data that included the entire population, then the values of the parameters would be known and no statistical inference would be required.

True

Is a paratmeter a constant?

Yes

Is the normal distribution continuous and symmetric in shape?

Yes

is mu a population parameter?

Yes

What does the expected value of Z equal?

Zero

What is a statistic?

a random variable

What is true about a sample statistic such as the same mean and sample proportion?

a sample statistic is a random variable

The Inverse Transformation, x= (mean) + z(standard deviation) is used to....

compute x values for given probabilites

A random variable X within an equally likely chance of assuming any value within a specified range is said to have which distribution?

continuous normal distribution

A random variable X with an equally likely chance of assuming any value within a specified range is said to have which distribution?

continuous uniform distribution

For a continuous random variable X, the function used to find the area under f(x) up to any value x is called the

cumulative distribution function

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

it is representative of the population we are trying to describe

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

larger

For a continuous random variable X, the cumulative distribution function F(x) provides the probability that X is

less than or equal to any value x

What are parameters?

the mean and standard deviation (or variance)

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

0.50

What theory allows us to use the normal probably distribution to approximate the sampling distribution of the sample mean whenever the sample size is large?

Central Limit Theorm

What does the variance equal?

One

Continuous random variables:

P(X=x)=0

The z table proves the cumulative probabilities for a given z. What does "cumulative probabilities" mean?

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

In a statistical problem, a population consists of

all items of interest

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

always normally distributed

A continuous random variable X can assume...

an infinite number of values over some interval

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

bell shaped

The probability that a discrete random variable X assumes a particular value x is

between zero and one

If a sample statistic constantly over -or -under estimates a population parameter, then there is......

bias

________ involves dividing a population into mutually exclusive and exhaustive groups, called clusters, and then selecting a random sample from these clusters for analysis.

cluster sampling

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

inferential statistics

The probability distribution of a continuous random variable is called its

probability density function

The probability distribution of a discrete random variable is called its...

probability mass function

The expected value of (p bar) is the

proportion of successes in the population

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

statistic, parameter

In ______, the population is divided up into stature and then randomly selected observations are taken proportionately from each stratum.

stratified random sampling

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

stratified random sampling

What kind of sampling is more likely to be used by political pollsters who want to ensure that each religious group is represented in the sample?

stratified random sampling

Random samples of size 400 are taken from a population whose population proportion is 0.25. The expected value of the sample proportion is...

0.25