BNAD 276 Connect Answers Chp 6-8
when the finite population correction factor is applied to the sample mean ,the resulting standard error for the sample mean is equal to
(o/ square root of n) square root (N-n)/(N-1)
for a 99% confidence interval a=
.01
a population has a mean of 50 and a standard deviation of 10. a random sample of 256 is selected, the standard error is x bar is equal to
.0625
random sample of size 400 are taken from a population whose population proportion of .25. the expected value of the sample proportion is
.25
random samples of size 100 are taken from a population whose proportion is 0.40. the expected value of the sample proportion is
.40
the required sample size for estimating a population proportion is largest when p^ equal
.50
a random sample of 60 observations result in 42 successes. what is the point estimate of the population proportion of successes
.7 p bar = 42/60= .7
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)
if an exponential distribution has the rate parameter A=5, then the expected value is
1/5
a population has a mean of 100 and a standard deviation of 12. a random sample of 36 is selected. the standard error is x bar is equal to
2
how many parameters are needed to fully describe any normal distribution
2
an investment strategy has an expected return of 12% and a standard deviation of 10%. if investment returns are normally distributed, the probability of earning a return of more than 32 percent is CLOSEST to
2.5% From the empirical rule, 95% of the returns fall between -8% and 32%, thus 5% of returns are treated that 32% or less than -8%. from symmetry, half of 5% or 2.5% will be greater than 32%
if the exponential distribution has an expected value equal to 5, then the standard deviation equals
5 E(X)=SD(X)
for a 95% confidence interval for the population mean, if samples of size n are drawn repeatedly from a given population, then
5% of the sample means will fall outside of the corresponding confidence interval
a sample of 25 is drawn from a normal population. a sample mean of 50 is calculated. for a 95% confidence interval, the margin of error is 10. a 95% confidence interval for the mean is
50 +- 10
for data that are normally distributed, the percentage of the data that falls within two standard deviations of the mean is
95%
CHAPTER 7
CHAPTER 7
CHAPTER 8
CHAPTER 8
if x has a normal distribution with u= 100 and o=5 then the probability P(100<X<110) can be expressed in terms of the standard normal random variable Z as
P(0<Z<2)
the probability that the normal random variable Z is less than 1.5 is equal to
P(Z>-1.5)
if Y=e^x has a lognormal distribution, what can be said of the distribution of the random variable X?
X follows a normal distribution
which of the following random variables is depicted with a bell-shaped curve
a normal random variable
which of the following is true about a sample statistic such as the sample mean or sample proportion
a sample statistic is a random variable
a sample is
a subset of the population
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
how does an interval estimator differ from a point estimator
an interval estimator provides a range of values for the population parameter whereas a point estimator provides a single value
the central limit theorem states that, for an distribution, as n get larger, the sampling distribution of the sample proportion
approaches a normal distribution
the probability that a discrete random variable X assumes a particular value x is
between zero and one
all of the following are characteristics of z and t df distribution EXCEPT
bimodal
for a continuous random variable X, the number of possible values
cannot be counted
the inverse transformation X=u+zo is used to
compute x values for given probabilities
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
suppose you were told that the delivery time of your new washing machine is equally likely over the time period 9am to noon. if we define the random variable X as delivery time, then X follows the
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
whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x bar and the
desired level of confidence
due to symmetry, the probability that the standard normal variable Z is greater than 0 is
equal to 0.5
the total area under the normal curve is
equal to 1
for a continuous 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
when a sample statistic is used to make inferences about a population parameter, it is referred to as
estimator
the poisson random variable counts the number of occurrences of an event over a given interval of time or space while the ---- is used to describe the time that elapses between such occurrences
exponential Distribution
a parameter is a numerical measure that describe a sample
false
the distinct values of both a continuous random variable and a discrete random variable can be counted
false
which of the following statements is the MOST accurate
for data that are normally distributed, 95% of the data will fall within 2 standard deviations of the mean
the most practical way to reduce the margin of error is to
increase the sample size
what does it mean to say that the exponential distribution is "memoryless"
it has a constant failure rate
a random variable X follows the continuous uniform distribution if
it has an equally likely chance of assuming any value within a specified range
the value of the finite population correction factor is always
less than one
alpha (a) is often referred to as the
level of significance
precision in interval estimate is implied by a(n) ---- margin or error
low
a confidence interval is constructed by using the point estimate as a base, to which we add and subtract the
margin of error
the probability distribution of a discrete random variable is called its probability
mass function
unlike the exponential distribution, the lognormal distribution has a failure rate that
may increase or decrease over time
as the samples size increases, the shape of the sampling distribution of p bar becomes
more normal
when comparing two confidence intervals, the one that has smaller margin of error has a
more precise estimate of the parameter
the exponential random variable is ________
nonnegative
when the sample size is sufficiently large, we can approximate the sampling distribution of the sample proportion using the
normal distribution
which of the following is an example of a continuous random variable
normal random variable
the exponential distribution is
not symmetric
the sampling distribution of the sample proportion can be approximated by a normal distribution when
np > or equal and n(1-p) > or equal 5
all of the following are component of the formula for selecting n to estimate p EXCEPT
o ^
the variance of the standard normal distribution is equal to
one
the exponential distribution is based entirely on
one parameter
the point estimator for the population proportion is
p bar
all of the following are components of the formula for selecting n to estimate u EXCEPT
p^
we use a sample statistic to make inference about an unknown population
parameter
what is the most typical form of a calculated confidence interval
point estimate +- margin of error
the two main components of a confidence interval are the
point estimate and margin of error
the probability distribution of a continuous random variable is called its
probability density function
a confidence interval can be interpreted as a
range of values used to estimate an unknown population parameter
we use the finite population correction factor of
reduce the sampling variation of x bar and p bar
a population consists of all items of interest in a statistical problem, whereas a ----- is a subset of the population
sample
a sample of n observations that have the same probability of being selected fro the population as any other samples of n observations is called a
simple random sample
the variance of x bar, which is equal to o^2/n is
smaller than the variance of the individual observation o2
a normal random variable X is transformed into Z by
subtracting the mean, and then dividing by the standard deviation
the two pieces of information that are necessary to determine the value of t df are
the level of significance and the sample size or degrees of freedom
if X is normally distributed with the mean=u and standard deviation=o then y=e^x has which distribution
the lognormal distribution
which of the following distributions is positively skewed and bounded below by zero
the lognormal distribution
if X is normally distributed random variable, then
the mean median and mode are all equal
the lognormal distribution is defined with reference to which distribution
the normal distribution
which of the following continuous and symmetric in shape
the normal distribution
which of the following can be represented by a discrete random variable
the number of defective light bulbs in a sample of 5
all of the following are examples of random variables that likely follow a normal distribution EXCEPT
the number of states in the USA
the exponential distribution is related to which distribution
the poisson distribution
the z table provides 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
a confidence interval narrows if the following is accomplished
the sample size increases and then chosen confidence levels decrease
what does it mean when we say that the tails of the normal curve are asymptotic to the x axis
the tails get closer and close to the x axis but never touch it
which of the following can be represented by a continuous random variable
the temp in florida during the month of july
stratified sampling is preferred to cluster sampling when the objective is
to increase precision
which of the following is an example of a population parameter
u
a managers of a women's clothing store is projecting next month's sales. her low-end estimate of sales is $25,000 and her high-end estimate is $50,000. she decides to treat all outcomes for sales between these two values as equally likely. if we define the random variable X as sales, then X follows the..
uniform distribution
cluster sampling works best
when most of the variation in a population is within groups and not between groups
when the confidence level increases from 95% to 99% the confidence interval for the population mean
widens
which of the following is an example of a sample statistic
x bar
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= u - zo
consider data that are normally distributed. in order to transform a standard normal value X into its unstandardized value Z, we use the following formula
z= x-u/o