Econ-E 370 Exam 2

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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


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