BNAD Ch. 1, 3, 7, 8 LearnSmart Questions
the mean of the standard normal distribution is equal to
zero
95% confidence interval for the population proportion is calculated as (0.40, 1.00) the margin of error for the interval is
0.30
the probability that a normal random variable X is less than its mean is equal to
0.50
Scenarios that use nominal scale
1- designating males as 1 and females as 2 compare gender performance on a test 2- noting the racial composition of an undergraduate class
for a 95% confidence the sample mean xbar will fall into the interval mu + or - (_____) x sigma over (sqr. n)
1.96
the height of the probability density function F(x) of the uniform distribution defined on the interval [A,B]
1/(B-A)
an investment strategy has an expected return of 12% and a standard dev of 10%. if an investment returns are normally distributed, the probability of earning a return less than 2% is closest to
16%
number of parameters that are needed to fully describe any normal distribution
2
sample mean and sample standard dev are calculated as 50 and 25. T=2.131 and there is a sample of 16
50 + or - 2.131(25/sqr. 16)
if x has a normal distribution with mu=100 and sigma=5, then the probability P(90<90<95) can be expressed in terms of the standard normal random variable Z as
P(-2<Z<-1)
it is known that the length of a certain product X is normally distributed with Mu=20 inches. How is the probability P(X>16) related to the probability P(x<16)
P(X>16) is greater than P(X<16) because the first is greater than 0.50 so P(X<16) is less than 0.50
it is known that the length of a certain product X is normally distributed with Mu=20 inches. how is P(x<20) related to the P(x<16)
P(x<20) is greater than P(x<16)
due to symmetry, the probability that the normal random variable Z is greater than 1.5 is equal to
P(z> -1.5)
Northern university college of business wants to determine the average starting salary for last years graduates. What is the population from which the survey is taken?
all of last years graduates from northern college of business
the interval scale of measurement
allows for the use of negative values
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 significant weakness of the ordinal scale is
an inability to measure differences between the ranked values
how does an interval estimator differ from a point estimator?
and 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 any distribution as N gets larger, the sampling distribution of the sample mean become
closer to a normal distribution
for a continuous random variable x, the function used to find the area under F(x) up to any value is called the
cumulative distribution funciton
some of the desireable properties of a point estimator si
efficeincy, unbiasedness, consistency
if an unbiased estimator is ____ its standard error must be lower than that of the other unbiased estimators
efficient
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 1
for a continuous random variable X, it is only meaningful to calculate the probability that the value of the random variable
falls within some specified inteval
a discrete random variable can assume an uncountable number of values
false
the sample size required to approximate the normal distribution depends on
how much the population varies from normality
stratified sampling is preferred to cluster sampling when the objective is to
increase population
the most practical way to reduce the margin of error is to
increase the sample size
The branch of statistics that draws conclusions about a large set of data based on a smaller set of data is often referred to as
inferential statistics
the normal distribution is completely described by these two parameters:
mean and variance
cluster sampling works best when
most of the variation in a population is within groups and not between groups
calculating standard dev of x bar
mu/sqr.n (mean/ square root sample size)
if we were to sample repeatedly from a given population, the average value of the sample mean will follow
normal
the estimator xbar folows a normal distribution when the underlying population follows a distribution
normal
the shape of the population from which a simple random sample is drawn is normal, then the shape of the sampling distribution of x bar is
normal
In general, we use sample data because
obtaining data from the population is often an expensive process
the probability of the sample mean is commonly referred to as the
sampling distribution of x bar
a sample of N observations that have the same probability of being selected from the population as any other sample of N observations is called a
simple random sample
for a given confidence level and standard dev, the width of the interval is wider for a
smaller sample size AND larger standard dev
when the finite population correction factor is applied to the sample proportion, the resulitng standard deviation for the sample mean is equal to
sqr. [P-(1-p)/N] * sqr. (N-n)/(N-1)
Which is DESCRIPTIVE statistics?
summarizing the variability of the exam scores of 40 students based on all 40 exam scores
Which is an example of INFERENTIAL statistics
testing the longevity of all light bulbs based on a sample of 100 light bulbs
a confidence interval narrow if the following is accomplished
the chosen confidence level decreases ALSO the sample size increases
all of the following are examples of random variables that likely follow a normal distribution except...
the number of states in the USA (this is not a variable)
the two pieces of info that are necessary to determine the value of T sub df are
the sample size or degrees of freedom ALSO the level of significance
bias refers to
the tendency of sample statistics to systematically over or under estimate a population parameter
if the expected value of an estimator is equal to the unknown parameter beign estimated, then the estimator is best characterized as an
unbiased estimator
a manager of a woman's clothing store... she decides to treat all outcomes for sales between these two values equally likely. If we define the random variable X as sales, then X follows the
uniform distribution
a characteristic of interest that differs among various observations is referred to as a
variable
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
a continuous random variable X follows the uniform distribution with a lower limit of a and an upper limit of b. The expected value of x
(A+B)/2
for a continuous random variable, one characteristic of its probability density function F(x) is:
F(x) < or equal to 1 for all values of x
the expected value and the variance of the standard normal random variable Z are both zero
FALSE, the expected value of Z is zero, but its variance is 1
as a general guideline, the normal distribution approximate can be used to describe the sampling distribution of the sample mean when
N> or equal to 30
the sample statistic Pbar is an estimator of
P
a parameter is a numerical measure that describes a population
True
if you have data that describes the entire population, then there is not need to make inference using sample data
True
which of the following random variables is depicted with a bell-shaped curve?
a normal random variable
which of the following statements is most accurate
a parameter is a constant although its value may be unknown
in a statistical problem, a population consists of
all items of interest
an estimator that tends to produce more accurate estimates of the population parameter as the sample size increases is best characterized as
consistent estimator
suppose you were told that the delivery time of your new washing machine is equally likely over the period of time from 9 am to noon. if we define the random variable X as delivery time then x follows a
continuous normal distribution
Number of people in a household
discrete variable
when a sample statistic is used to make inferences about a population parameter, it is referred to as:
estimator
if X is normally distributed with expected value mu and standard deviation sigma, then x bar is normally distributed with
expected value of mu and standard deviation of sigma/sqr. N
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 u is referred to as the
level of significance
the expected value of xbar is equal to
mu
the value of the finite population correction factor is always less than
one
the variance of the standard normal distribution is equal to
one
A ______ includes all items of interest in a statistical problem
population
the paramter P represents the
population proportion
selection bias occurs when
portions of the population are excluded from the consideration for the sample
the probability distribution of a continuous random variable is called its
probability density function
if X is a normally distributed random variable then...
the mean the median and the mode are all equal
a company wants to estimate the mean price of oil over the past 10 years. what kind of data does the company need?
time series data
the expected value of x bar is equal to mu (the mean)
true
if x is normal, we can transform it into the standard normal random variable as
z= (xbar-mu)/(sigma/sqr. n)
Samples are primarily used to
Make inferences about population parameters
for any population proportion P, the sampling distribution of the sample proportion is approximately normally distributed if
NP > or equal to 0.05 N
The inverse transformation, X=mu+Z(sigma) is used to______
compute X values for given probabilities
the inverse transformation, x=mu +z(sigma) is used to
compute x values for given probabilities
a continuous random variable has the uniform distribution on the interval [A,B] If it's probability density function F(x)
is constant for all x between A and B
which of the following is true about a sample statistic such as sample mean or sample proportion
it is a random varaible
when the population standard deviation is unknown, the standard error for the sample mean is
s/(sqr.N)
which of the following scenarios is an example of the interval scale?
the outside temperature (in degree Fahrenheit)
what does cumulative probabilities mean?
the probability that Z is less than or equal to a given z value
which of these is a characteristic of a "bad" sample
the sample is not representative of the population we are trying to describe
for a given sample size and standard deviation, the width of the confidence interval is _____ for a greater confidence level
wider
the probability distribution of the sample mean is commonly referred to as
xbar
an investment strategy that 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% is closest to:
2.5%
a 95% confidence for the pop mean is calculated as (40, 80) the point estimate for this interval is
60 because (40+80)/2= 60
due to symmetry, the probability that the standard normal random variable Z, is less than zero is equal to
0.50
the area under the normal curve below its expected value is
0.50
a 95% confidence interval for the population mean implies that
for repeated samples, 95% of the sample means will fall within the interval
for a continuous random variable x, how many distinct values can it assume over an interval?
infinite
which of the following is an example of a continuous random variable?
normal random variable
in order to derive a confidence interval for mu, the estimator x bar must have a
normal sampling distribution
all of the following are examples of cross-sectional data except:
quarterly sales for a computer company for t he last five years
a research analyst collects data on the weekly closing price of gold throughout the year, the scale of data is
ratio
the central limit theorm state that the distribution of the sample mean will be approximately normal if
the sample size is sufficiently large as a general guideline N> or equal to 30
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 closer to the x axis but never touch it
the lower the confidence interval, the narrower the confidence interval
true
which is an estimate
xbar=20
