MGSC 291

It systematically over or under estimates the unknown parameter being estimated

A sample statistic is considered biased if

More normal

As the sample size increases, the shake of the sampling distribution of p bar becomes

Falls within some specified interval

For a continuous random variable X it is only meaningful to calculate the probability that the value of the random variable

It's a discrete distribution (the normal distribution is a continuous distribution)

All of the following are characteristics of the normal distribution except: It is completely described by 2 parameters It is a discrete distribution It's symmetric around it's mean It's asymptotic

Cannot be counted

For a continuous random variable X, the number of possible values

It is smaller and therefore suggests that averages have less variation than individual observations.

How does the variance of the sample mean compare to the variance of the population?

2

How many parameters are needed to fully describe any normal distribution

Expected value (µ) and std dev (σ/ square root of n)

If X is normally distributed with expected value and std dev then x bar is normally distributed with

For any sample size n, the sampling distribution of the sample mean is normally distributed.

If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?

All items of interest

In a statistical problem, a population consists of

function that assigns numerical values to the outcomes of an experiment

Random variable

There is a systematic exclusion of certain groups from consideration for the sample

Selection bias occurs when

Random variable

Statistic

Estimator

When a sample statistic is used to make inferences about a population parameter, it is referred to as a/an

Probability density function

The probability distribution of a continuous random variable is called its

Between zero and one

The probability that a discrete random variable X assumes a particular value x is

0.5

Due to symmetry the probability that the standard normal random variable Z is less than 0 is equal to

Cumulative distribution function

For a continuous random variable X the function used to find the area under f(x) up to any value x is called the

Infinite

For a continuous random variable x, how many distinct values can it assume over an interval? Infinite Countably infinite finite countably finite

characterized by uncountable values of an interval

continuous random variable

The sample size is sufficiently large; as a general guideline n>= 30

The central limit theorem states that the distribution of the sample mean will be approximately normal if

Equal to 1

The total area under the normal curve is

Smaller than the variance of the individual observation σ^2

The variance x bar which is equal to σ^2/n is

The probability that Z is less than or equal to a given z value

The z table provides the cumulative probabilities for a given z. What does cumulative probabilities mean?

Normal random variable

Which of the following random variables is depicted with a bell shaped curve? Normal random variable Binomial random variable Exponential random variable Uniform random variable

.5

The probability that a normal random variable X is less than it's mean is equal to

0.5

The probability that a normal random variable is less than its mean is ____.

1. the probability of each value x is a value between 0 and 1 2. the sum of the probabilities equals 1

2 properties of discrete probability distributions

simple random samples stratified random samples cluster random samples

3 types of sampling methods

Constant for all x between a and b, and 0 otherwise

A continuous random variable has the uniform distribution on the interval a, b if it's probability density function is

Simple random sample

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(n)

n>=30

As a general guideline, the normal distribution approximation can be used to describe the sampling distribution of the sample mean when

A particular value of an estimator

Estimate

Constant

Parameter is a

if a number of options have similar expected values, they choose the one with the lowest risk

Risk averse

they will choose an option with negative expected value if one of its possible outcomes is large, but risky

Risk loving

consumers are indifferent to risk, they always choose the option with the largest expected value, regardless of risk.

Risk neutral

assumes a countable number of distinct values

discrete random variable

consists of all items of interest; is a constant but is often unknown

population

a subset of the population

sample

A continuous random variable has a probability density function, and a discrete random variable has a probability mass function.

Which of the following is correct? -A continuous random variable has a probability density function but not a cumulative distribution function. -A discrete random variable has a probability mass function but not a cumulative distribution function. -A continuous random variable has a probability mass function, and a discrete random variable has a probability density function. -A continuous random variable has a probability density function, and a discrete random variable has a probability mass function.

f(x) is symmetric around the mean

Which of the following is not a characteristic of a probability density function f(x)? -f(x) ≥ 0 for all values of x. -f(x) is symmetric around the mean. -The area under f(x) over all values of x equals one. -f(x) becomes zero or approaches zero if x increases to +infinity or decreases to −infinity.

Information from the sample is typical of information in the population

Which of the following is not a form of bias? -Portions of the population are excluded from the sample. -Information from the sample is typical of information in the population. -Information from the sample overemphasizes a particular stratum of the population. -Those responding to a survey or poll differ systematically from the nonrespondents.

A statistic is a random variable

Which of the following is true about statistics such as the sample mean or sample proportion? -A statistic is a constant. -A statistic is a parameter. -A statistic is always unknown. -A statistic is a random variable.

To increase precision

Stratified sampling is preferred to cluster sampling when the objective is

False ( a continuous random variable assumes an infinite number of values over an interval.)

T or F the distinct values of both a continuous random variable and a discrete random variable can be counted

False (the expected value of Z is zero, but the variance is 1)

T or F the expected value and the variance of the standard normal random variable Z are both zero

Closer to a normal distribution

The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean becomes

Sampling distribution of x bar

The probability distribution of the sample mean is commonly referred to as the

How much the population varies from normality

The sample size required to approximate the normal distribution depends on

The tails get closer and closer to the x axis but never touch it.

What does it mean when we say that the tails of the normal curve are asymptotic to the x axis?

It is representative of the population we are trying to describe

What is a primary requirement for a "good" sample?

The number of defective light bulbs in a sample of five

Which of the following can be represented by a discrete random variable? The circumference of a randomly generated circle The time of a flight between Chicago and New York The number of defective light bulbs in a sample of five The average distance achieved in a series of long jumps

X bar

Which of the following is considered an estimator? X bar µ σ σ2