QMB 3200 Bliss Exam 2

The numerical value obtained for x ̅ , s, or p ̅ is called the:

Point estimator

In the EAI example(ch 7), this is a finite population of 2,500 managers (elements). The variables include salary and yes or no to a training program. For the population, the mean salary is $51,800 and the standard deviation is $4,000. The proportion of managers that have completed training is 60%. To summarize: and Do a RAND for EAI:

u = $51,800, σ=$4,000, P = .6 Do a RAND for EAI. x ̅ =$51,089 s =$4,204 p ̅ = .57

Statistics Involve: Inferential which is?

using a sample to make a determination about the population parameters.

The sample mean , is the:

point estimator for the population mean, u

Point estimation is known as a:

statistical inference

With sampling distribution, as n (sample size) increases:

the distribution of the x ̅ and p ̅ becomes approximately normal.

Sampling Methods: cluster sampling

the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes observations from randomly selected clusters.

Sampling Methods: 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. The number of observations per stratum is proportional to the stratum's size in the population. The data for each stratum are eventually pooled.

True or False: The standard error of x ̅ and p ̅ DECREASES as we INCREASE n

True, because when you increase the sample size you decrease variability.

Sample distribution Properties: Sample Proportion formula

Up ̅=p(true proportion)

Selecting a Sample: infinite population.

An infinite population is excessively large, or continually changing and there is no limit to the elements that can be generated. We must select a random sample in order to make a valid statistical inferences about the population which the sample is taken.

Standard Error means:

How much group statistics vary (not just a single item)

With sampling distributions:

If you know what the whole pizza looks like, then I can tell you how likely certain pieces are to occur.

Sample distribution Properties: Standard error(sample proportion)

SEp ̅=σp ̅= SQRT p(1-p)/n

Sample distribution Properties: Standard error(sample mean)

SEx ̅=σx ̅=σ/sqrt of n (sample size)

Examples of a finite population:

They are often defined by list such as: Organization membership roster, Credit card account numbers, and Inventory product numbers.

True or False: With sampling distribution, the mean of the sampling distribution does NOT depend upon n

True

True or False: With sampling distribution, we know the distribution of these values.

True

Sample distribution Properties: Sample Mean formula

Ux ̅=U

Central Limit Theorem:

When the population from which we are selecting a random sample does not have a normal distribution, the central limit theorem is helpful in identifying the shape of the sampling distribution of x ̅

Sampling Methods: Using Excel

a Random Number generator method (RAND) and then sort from either low to high, or high to low, and this will give you a sample without replacement.

In selecting random samples of size n from a population, the sampling distribution of the sample mean x ̅can be approximated by:

a normal distribution as the sample size becomes large.

In most applications, the sampling distributions of x ̅ can be approximated by:

a normal distribution whenever the sample size is 30 or more

Selecting a Sample: Simple random sample

a sample of n observations which has the same probability of being selected from the populations as any other sample of n observations. Most statistical process involve this.

A good (random) sample is:

a sample that is representative of the population without bias. Also known as probability samples.

The best sampling method is?

a simple random sample, using the EXCEL RAND function.

Nonresponse bias refers to:

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

Selection bias refers to:

a systematic exclusion of certain groups from consideration for the sample.

A Population?

consists of all items of interest in a statistical problem.

Statistics involve: Descriptive statistics which is?

describing the data, usually in a tabular or graphical format.

A particular value of the estimator is called an:

estimate

When a statistic is used to estimate a parameter, it is referred to as an:

estimator

The sampling distribution of x ̅has an:

expected value or mean, a standard deviation, and expected shape.

In sampling distribution, the parameter is a:

fixed value, so it does not have a distribution

Symbols: u

is the mean for the population

Symbols: p ̅

is the proportion for the sample

Symbols: x ̅

is the sample mean

Symbols: s

is the sample standard deviation

Symbols: σ

is the standard deviation of the population

Symbols: p

is the true proportion of the population

The key point to sampling is:

it makes an inference about a population.

A sample(statistic) is used to:

make inferences about a unknown population parameter.

Sampling is used to:

make inferences about these parameters.

When the population has a normal distribution, the sampling distribution of x ̅ is:

normally distributed for any sample size

In regards to sampling, Two primary areas of interest are:

population means and population proportions.

example of a infinite sample

population of the USA

The sample proportion , is the point estimator of the:

population proportion, p.

The sample standard deviation s, is the point estimator for the:

population standard deviation, σ

The sampling distribution of x ̅is the:

probability distribution of all possible values of the sample mean x ̅

Simple random sample of size n from a finite population of size N is a...

sample selected such that each possible sample of n has the same probability of being selected.

A random sample from a infinite population is a....

sample selected such that the following conditions are satisfied: 1. each element selected comes from the population of interest 2. each element is selected independently

In cases where the population is highly skewed or outliers are present:

samples of size 50 may be needed

The symbols σx ̅ is referred to as:

standard error of the mean

Symbols: N (for x ̅)

the population size

The sampling distribution of p is:

the probability distribution of all possible values of the sample proportion p.

Point Estimation is?

the procedure to determine the sample mean, standard deviation and proportion is known as point estimation. The values that are determined are known as the point estimate.

Symbols: n (for x ̅)

the sample size

BIAS refers to:

the tendency of a sample statistic to systematically over or under estimate a population parameter.

In sampling distributions, if you take the standard deviations of the sample means, your standard deviations:

would be less than the standard deviation of the population.

if you take all of the sampling distributions and prepare a frequency distribution then:

you would get a normal bell curve with the most frequent observations being near the mean of the population and the proportion of the population.

The notation for standard deviation of x ̅ is:

σx ̅

The mean is also known as:

Expected Value

Sampling Distribution: Using Xbar

(sample mean), this is quantitative data

Sampling Distribution: Using Pbar

(sample population)Yes/No data or categorical data

A random sample needs the following conditions:

Each element selected comes from the same population, and Each element is selected independently.

Selecting a Sample: finite population

A finite population has limits and you can develop a list of all possible elements in the population.

The most critical thing to do in a simple random sample is?

Remove as much Bias as possible to get a good sample

A Sample?

is a subset of the population.

With a sampling distribution properties for the sample mean, it is approximately normal if:

1. N>= 30 (look like a bell curve) OR 2. Population from which data came from is roughly normal

process of statistical inference

1. Population with a mean 2. A simple random sample of n elements is selected from the population 3. The sample data provides a value for the sample mean x ̅ 4.The value of x ̅ is used to make inferences about the value of the mean.

With a sampling distribution properties for the sample proportion, it is approximately normal if:

1. n multiplied by p>=5 AND 2. n(1-p)>=5 n= sample size p=true proportion

The Expected value of P is:

E(p)=p Where p is the population proportion

The expected value of x ̅is:

E(x ̅)= mean

When the population from which we are selecting a random sample does not have a normal distribution, the ____________________________ is helpful in identifying the shape of the sampling distribution of x ̅

central limit theorem