Lecture 7

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 variable

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 deviation𝜎 𝑛.

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.