Lecture 7 and 8

sampling plan, experimental design

sampling plan, experimental design

The way a sample is selected is called the _______ or _______.

simple random sampling

_______ is a commonly used sampling plan in which every sample of size n has the same chance of being selected.

simple random sample

If the sample of n = 2 observations is selected so that each of these six samples has the same chance—one out of six or 1/6—of selection, then the resulting sample is called a _______, or just a random sample.

random, simple random sample

If a sample of n elements is selected from a population of N elements using a sampling plan in which each of the possible samples has the same chance of selection, then the sampling is said to be _______ and the resulting sample is a _______.

observational study

The situation described in the example is called an _______ because the data already existed before you decided to observe or describe it.

surveys

Most sample _______, in which information is gathered with a questionnaire, fall into this category.

strata, stratified

When the population consists of two or more subpopulations, called _______, a sampling plan that ensures that each subpopulation is represented in the sample is called a _______ random sample.

cluster

Another form of random sampling is used when the available sampling units are groups of elements, called _______.

clusters

A cluster sample is a simple random sample of _______ from the available clusters in the population.

ordered

Sometimes the population to be sampled is _______, such as an alphabetized list of people with driver's licenses, a list of utility users arranged by service addresses, or a list of customers by account numbers.

1-of-k

A _______ systematic random sample involves the random selection of one of the first k elements in an ordered population, and then the systematic selection of every kth element thereafter.

convenience

_______ sample — a sample that can be easily and simply obtained without random selection.

statistics

When you select a random sample from a population, the numerical descriptive measures you calculate from the sample are called _______.

random variables

These statistics vary or change for each different random sample you select; that is, they are _______.

sampling

The probability distributions for statistics are called _______ distributions.

central limit theorem (CLT)

One important statistical theorem that describes the sampling distribution of statistics that are sums or averages is the _______.

normal

Under rather general conditions, this theorem states that sums and means of random samples of measurements drawn from a population tend to have an approximately _______ distribution

central limit theorem (CLT)

This phenomenon is the result of an important statistical theorem called the _______.

mew(μ), sigma over square root of n

If random samples of n observations are drawn from a nonnormal population with finite mean μ and standard deviation σ, then, when n is large, the sample mean follows a normal distribution with mean _______ and standard deviation _______.

normal, n times mew, square root n times sigma

The Central Limit Theorem can be restated to apply to the sum of the sample measurements Σx i , which, as n becomes large, also has an approximately _______ distribution with mean _______ and standard deviation _______.

normal

If the sampled population is _______, then the sample mean is normal no matter what the size is

symmetric

When the sampled population is approximately _______, the sampling distribution of 𝑋 is normal for a relatively small n.

skewed

When the sampled population is _______, the sample size n must be larger (at least 30) in order for 𝑋 to be approximately normal.

standard error, error

The standard deviation of a statistic used as an estimator of a population parameter is also called the _______ of the estimator because it refers to the _______ of the estimator.

estimation

_______: Estimating or predicting the value of the parameter

hypothesis test

_______: Making a decision about the value of a parameter based on some preconceived idea about what its value might be

estimator

An _______ is a rule, usually expressed as a formula, that tells us how to calculate an estimate based on information in the sample.

point estimator, interval estimator

There are two types of estimators: _______ (a single number is calculated to estimate the population parameter) and _______ (two number are calculated to form an interval within which the parameter is expected to lie).

unbiased, biased

A point estimator is said to be ____________ if the mean of its distribution is equal to the true value of the parameter being estimated. Otherwise, the estimator is said to be _________.

spread

The ___________ (as measured by the variance) of the estimator's sampling distribution should be as small as possible.

error

The distance between an estimate and the true value of the parameter is called the _________ of estimation.

population mean, mean

The parameter we are interested in is a _______ 𝜇. To estimate it, we can use the sample _______, 𝑋 bar.

point

This 𝑋 bar is a _______ estimator.

unbiased

Point Estimator This |X is a point estimator. It is _______ (biase/unbiase).

sigma over square root of n

Its standard error (SE) is _______.

11.1

If we just use one single value, our guess would be $_______. And this is the point estimator we studied before.

margin of error

We call the size of the wiggle room _______.

confidence

Also, we want to associate a value 𝛼 to this interval. This 𝛼 corresponds to a probability. (1- 𝛼), the probability that the true value 𝜇 falls in this interval, is called _______.

normal

The sample size is large enough. CLT applies. So we can work with _______ distributions.

wider

1 − 𝛼 is the probability that the interval covers the true value. The smaller the 𝛼 is, the _________ the interval is.

narrower

If n increases, the interval is getting __________. This is because large n means more information, therefore less uncertainty.