Econ-E 370 Exam 2
The probability that a continuous random variable equals a specific value is always equal to 1
False
The sampling distribution of the mean describes the pattern that individual observations tend to follow when randomly drawn from a population
False
The standard deviation of the normal distribution is equal to the mean of this distribution
False
With the normal probability distribution, the probability over any interval in the distribution is equal to any other interval with the same width
False
It is known that the length of a certain product x is normally distributed with a mean= 20 inches. How is the probability P(x>16) related to P(x<16)?
P(x>16) is greater that P(x<16)
A convenience sample is an example of a nonprobability sample
True
A sample median is an example of a statistic
True
An Internet poll, where individuals may respond to a survey as many times as they choose to, is an example of a nonprobability sample
True
Cluster sampling can be used to test market new products with clusters which correspond to some geographical areas
True
Continuous random variables are outcomes that take on any numerical value in an interval as a result of conducting an experiment
True
Continuous random variables can take on values between whole integers that contain decimal points
True
Given that the probability distribution is normal, it is completely described by its mean μ and its standard deviation σ
True
In Excel, P(x > 5) and P(x ≥ 5) from the normal distribution can be computed using the same function
True
The area under the curve of the normal probability distribution is always equal to 1
True
The normal probability distribution is symmetric and bell-shaped
True
The probability density function of a continuous random variable is used to describe the random variable and is the counterpart to the probability function of a discrete random variable
True
The standard deviation of x prime (standard error of the sample mean) equals the population standard deviation divided by the square root of the sample size if the population is infinite
True
The values for the normal random variable can be positive or negative
True
Sampling distribution of sample x is the
probability distribution of the sample mean
A smaller standard deviation for the normal probability distribution results in a
skinnier curve that is tighter and taller around the mean
The standard deviation of the sampling distribution of sample x is called the
standard error of the mean
Sampling distribution describes the distribution of
statistics
For a continuous random variable x, the probability density function f(x) represents
the height of the function at x
How does the variance of the sample mean compare to the variance of the population?
It is smaller and therefore suggests that averages have less variation than individual observation
If x has a normal distribution with mean= 100 and SD= 5, then the probability P(90<=x<=95) can be expressed in terms of a standard normal variable z as
P(-2<=z<=-1) (90-100)/5= -2 (95-100)/5= -1
Which of the following can be represented by a continuous random variable
The time of a flight between Chicago and New York
Excel's function NORM.DIST is used to compute the area on the left of a given number under the normal curve
True
For any population proportion p, the sampling distribution of will be approximately normal if the following conditions hold: np ≥ 5 and n(1 − p) ≥ 5
True
For continuous distributions, the probability that x is less than or equal to a value is the same as the probability that x is less than that value
True
In stratified random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called strata. A stratified sample includes randomly selected observations from each stratum, which are proportional to the stratum's size
True
It is known that P(x ≤ x0) = 0.7 for a normally distributed random variable x with the mean μ and the standard deviation σ. To compute the value of x0, you could use the following Excel function: = NORM.INV(0.7, μ, σ)
True
Sampling without replacement means that once a member of a population is chosen for a sample, it cannot be chosen again for the same sample
True
The mathematical expression that describes the shape of normal curves is known as the normal probability density function
True
The sample means for a population that follows the normal distribution will also be normally distributed, regardless of the size of the samples
True
The sampling distribution of the proportion describes the pattern that sample proportions tend to take on when randomly drawn from a population
True
The standard error of the mean is the sample mean standard deviation, which measures the variation around the mean of the sample means
True
The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to one
True
The z-score in a normal probability distribution determines the number of standard deviations that a particular value, x, is from the mean
True
We expect the average value of many sample means to be close to the population mean from which they were drawn
True
When the proportion of sample size to population size, n/N, is greater than 5%, the finite population correction factor is used to adjust the standard error of the proportion
True
For any continuous random variable, the probability that the rand variable takes on exactly a specific value is
Zero
The center of a normal curve
is the mean of the distribution
What is the relationship between the expected value of the sample mean and the expected value of the population
mean of sample x = mean of population
The Normal distribution can approximate the binomial distribution as long as
np>=5, nq>=5
The Central Limit Theorem (CLT) states that
Sample means of large sized samples will be normally distributed regardless of the shape of their population distribution
What is the relationship between the SD and the sample mean and the population SD
Sample x SD = (Population SD)/sqrt(sample size)
Any normally distributed values can be standardized with z-scores
T
Continuous random variable may assume:
any value in an interval or collection of intervals
Which of the following is NOT a characteristic of the normal probability distribution
the standard deviation must be 1
For the standard normal probability distribution, the area to the left of the mean is
0.5
In a standard normal distribution, the probability that z is greater than 0 is
0.5
A parameter is a random variable, whereas a sample statistic is a constant
False
A population mean is an example of a statistic
False
As the sample size decreases, the standard error of the proportion will also decrease
False
Cumulative distribution function and probability density functions for the normal distribution are not related
False
Excel's functions NORM.DIST(5, 4, 1, TRUE) and NORM.DIST(5, 4, 1, FALSE) calculate the same result
False
For any population x with expected value µ and standard deviation σ, the sampling distribution of will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n < 30
False
For any sample size n, the sampling distribution of is normal if the population from which the sample is drawn is uniformly distributed
False
For the standard normal distribution, P(z > 2) is bigger than P(z > 1)
False
If the population does not follow the normal probability distribution, the Central Limit Theorem tells us that the sample means will be normally distributed with sufficiently large sample size. In most cases, sample sizes of 5 or more will result in sample means being normally distributed, regardless of the shape of the population distribution
False
In Excel, P(x > 5) can be computed as = 1 - NORM.DIST(6, mean, SD, TRUE)
False
In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes randomly selected observations from each cluster, which are proportional to the cluster's size
False
It is known that P(x > x0) = 0.7 for a normally distributed random variable x with the mean μ and the standard deviation σ. To compute the value of x0, you could use the following Excel function: = 1 - NORM.INV(0.7, μ, σ)
False
The continuity correction factor allows us to approximate the binomial distribution with the exponential distribution by adding and subtracting the value 0.5 to create the interval of
False
The higher the standard error of the mean, the less variation you will notice from one sample mean to the next as they are drawn from the population
False
The letter z is used to denote a random variable with any normal distribution
False
The standard deviation of x prime suggests that the variation between observations is smaller than the variation between averages
False
The z-score follows a normal distribution with μ = 1 and σ = 0, which is known as the standard normal distribution
False
To use the Central Limit Theorem, we need to know the mean and standard deviation of the population
False
We are often interested in finding the probability that a continuous random variable assumes a particular value
False