Econ391 Exam 1

Strata

(groups) are chosen specifically to represent different characteristics within the population, such as ethnicity, location, age, or occupation.

normal distribution

- bell shaped curve - total area = 1 - symmetrical

random variables

- may be classified as discrete - assumes a countable number of distinct variables ex: rolling a die/ flipping a coin

why do we need to sample?

- obtaining information on the entire population is expensive - it is impossible to examine every member of the population

standard normal distribution

- μ (the mean) = 0 - σ (the standard deviation) = 1

B0

-Y intercept -tells us the value if Y when X is 0

the value of the ________ is used to estimate the value of the population parameter

...

systematic sampling

Choose a starting point randomly and then systematically take objects at a certain number apart. Advantage: Easier to administer than simple random samples and are usually a good approximation of a random sample. Disadvantage: If there is a pattern in the population then certain objects could be chosen more or less often than others.

Which of the following is not a characteristic of the normal probability distribution? A) The mean of the distribution can be negative, zero, or positive. B) The distribution is symmetrical. C) The mean, median, and mode are equal. D) The standard deviation must be one.

D

cluster sampling

Divide the population into mutually exclusive and collectively exhaustive groups, called clusters. - Randomly select clusters. - Sample every observation in those randomly selected clusters.

stratified random sampling

Divide the population into mutually exclusive and collectively exhaustive groups, called strata. Randomly select observations from each stratum, which are proportional to the stratum's size.

Mode

The value that occurs most frequently in a given data set. - can occur at two or more different values

population parameter

a numerical measure that describes an aspect of a population -usually unknown

A numerical measure from a population, such as a population mean, is called ____

a parameter

sample

a subset of the population

census

a survey that measures the entire target population

The sampling distribution describes the

long-run behavior of a statistic.

the _________ is the measure of location most often reported for property value data and annual income.

median (because a few extreme property values can inflate the mean)

B1<0

negative relationship between X and Y

B1=0

no relationship between X and Y

deterministic linear relationship

represented by a straight line

In point estimation, data from the

sample are used to estimate the population parameter

A probability distribution for all possible values of a sample statistic is known as a _____.

sampling distribution

A sample chosen by stratified random sampling involves

selecting a simple random sample from each of a given number of strata formed from the elements in the population.

B1

slope

sampling bias

the tendency of a sample statistic to systematically over- or underestimate a population parameter.

median

the value in the middle of the data set where the data items are arranged in ascending order. - whenever a data set has extreme values, the median is the preffered measure of central location

changing the x value to a z value

use Z-formula 1) Take your x-value and subtract the mean (μ) 2) Divide it by the standard deviation (this gives you the z-value or z-score)

Which of the following symbols represents the mean of a sample?

x̄

unbiased sample

1. The idea is for each object in the population to be equally likely to be chosen as part of the sample. 2. The sample should also be representative of the population (if the population was 2/3 red and 1/3 green then the sample should be equally split)

A negative value of z indicates: A) the number of standard deviations an observation is below the mean. B) a mistake has been made in computations, since z cannot be negative. C) the number of standard deviations an observation is above the mean. D) the data has a negative mean.

A

For the standard normal probability distribution, the area to the left of the mean is: A) 0.50 B) any value between zero to one. C) -0.50 D) 1.00

A (cant have negative area)

nonresponse bias

A systematic difference in preferences between respondents and non-respondents to a survey or a poll.

selection bias

A systematic exclusion of certain groups from consideration for the sample. The sample is not representative of the population intended to be analyzed.

stratified random sampling part 2

Advantage: It can lead to a very good random unbiased representative sample. Guarantees that the each population subdivision is represented in the sample. Disadvantage: Expensive. Complex to administer. A considerable amount of information about the population is required. Note: Political pollsters often employ stratified random sampling in an attempt to ensure that each: Area of the country, ethnic group, religious group, etc. is appropriately represented in the sample.

cluster sampling part 2

Advantage: Less expensive than other sampling methods. More convenient and practical than simple random sampling. Useful when clusters occur naturally in the population (i.e. city blocks, school, and other geographic areas) Useful when most of the variation is within groups, not between groups. Disadvantage: Less precision than simple random sampling or stratified sampling. If the clusters are different from each other with regard to the elements that we are measuring it can lead to bias or non-representativeness.

convenience sampling

Randomly survey students walking on campus or shopping mall. - Take the next 20 objects off the production line. Advantage: They are convenient For a cheap and quick poll it may not really matter. Disadvantage: They are often bias in some way

regression analysis

Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

stratified vs cluster sampling

Stratified Sampling: • Sample consists of elements from each group. • Preferred when the objective is to increase precision. Cluster Sampling • Sample consists of elements from the selected groups. • Preferred when the objective is to reduce cost

the median for an even number of observations

add two middle values together and divide by 2.

descriptive statistics

are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire or a sample of the population. -can be broken down into measures of central tendency and measures of variability

inferintial statistics

are used by taking a random sample of data from a population to describe and make inferences about the population

sample statistic

calculated from sample and used to make inferences about the population

Regression analysis

can be used to develop an equation showing how the variables are related

A wildlife management organization is interested in estimating the number of moose in a particular region. Organization employees divide the region into 10 sections and randomly select four sections to survey the number of moose present. What sampling method is being used?

cluster sampling

Population

consists of all items of interest in a statistical problem

Random Variables may also be classified as ....

continuous -The random variable is characterized by (infinitely) uncountable values within any interval. ex: weight and hieght of new born babies

Two branches of statistics

descriptive and inferential

A simple random sample from a process (an infinite population) is a sample selected such that _____.

each element selected comes from the same population and each element is selected independently

regression analysis is used to determine

if a linear relationship exists between two quantitative variables

sample statistic

if the measures are computed for data from a sample -referred to as the point estimator of the corresponding population parameter

population parameter

if the measures are computed from a population

coefficient of variation

indicates how large the standard deviation is in the relation to the mean

simple random sample

is a sample of n observations which has the same probability of being selected from the population as any other sample of n observations. - It is theoretically the ideal method of sampling. Advantage: This produces an unbiased sample. Can be easily implemented in manufacturing populations. Disadvantage: we hope it is a representative sample.

null hypothesis

is a tentative assumption about a population parameter.

stochastic (probabilistic) relationship

is one in which one value of X may be associated with several different values of Y for different data points. -In short, there is an underlying linear relation between X and Y, but Y is subject to some external "noise".

the purpose of statistical inference is to provide information about the

population based upon information contained in the sample

Selection bias occurs when ________

portions of the population are excluded on the sample

B1 > 0

positive relationship between X an Y

A probability sampling method in which we randomly select one of the first k elements and then select every kth element thereafter is _____.

systematic sampling

The population we want to make inferences about is the ______

target population

standard deviation

tells us how measurements for a group are spread out from mean or the expected value -positive square root of the variance

normal distribution: asymptotic

that is, the tails get closer and closer to the horizontal axis, but never touch it.

Variance

the average of the squared differences between each data value and the mean - measure of variability - useful in comparing the variability of two or more variables

mean

the average value of a group of numbers -The sample mean 𝒙bar is the point estimator of the population mean µ.

the bigger the sample...

the closer the estimate to your parameter

if the data have exactly 2 modes

the data are bimodal

if the data have more than two modes

the data are multimodal

range

the difference between the highest and lowest data values - simplest measure of variability - very sensitive to the smallest and largest data values

alternative hypothesis

the opposite of what is stated in the null hypothesis. - is the research hypothesis

Stratified random sampling is a method of selecting a sample in which _____.

the population is first divided into groups, and then random samples are drawn from each group