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