Chapter 7

How do you find the point estimate of the population mean?

find the mean of the sample

How do you find the point estimate of the proportion in the population?

find the proportion in the sample

How do you find the point estimate of the population standard deviation?

find the standard deviation of the sample

Would this be a sampling from a finite or infinite population: Obtain a sample of licensed drivers in the state of New York?

finite

Would this be a sampling from a finite or infinite population: Obtain a sample of students in a statistics course at Indiana University?

finite

relative efficiency

given two unbiased point estimators of the same population parameter, the point estimator with the smaller standard error is more efficient

Does the point estimator with the smaller standard error have the smaller or greater relative efficiency?

greater

Would this be a sampling from a finite or infinite population: Obtain a sample of boxes of cereal produced by the breakfast choice company?

infinite

A sample size of 100 is selected from a population with p=.40. What is the expected value of P?

.40

What conditions are required for a random sample?

1) each element selected comes from the same population 2) each element is selected independently

what are the 3 properties of a good point estimator?

1) unbiased 2) efficiency 3) consistency

A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample mean x will be used to estimate the population mean. What is expected value of x?

200

What size does the sample need to be for the sample distribution to have a relatively normal distribution?

30 or more, however if the population is highly skewed or outliers are present, samples of 50 or more may be needed.

Standard deviation of the sample proportion or standard error of the sample proportion

=Sqrt(p*(1-p)/n)

A sample size of 100 is selected from a population with p=.40. What is the standard error of p?

=sqrt(.4*(1-.4)/100) =0.049

A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample mean x will be used to estimate the population mean. What is the standard deviation of x?

=std. dev of population/ square root of n =50/sqrt(100) = 5

Formula for standard error

=std. deviation/square root of n

Formula for sample proportion

=x/n

Central Limit Theorem

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

Assume a finite population has 350 elements. Using the last three digits of each of the following five digit random numbers, determine the first four elements that will be selected for the simple random sample. 98601 73022 83448 02147 34229 27553 84147 93289 14209

Step 1) break out the last 3 digits of each 5 digit random number 601 022 448 147 229 553 147 289 209 Step 2) The numbers must be less than or equal to 350, discard all numbers over 350, and you are left with 22 147 229 289 209 Step 3) Select the first 4 numbers 22 147 229 289

If the population you are selecting a random sample from does not have a normal distribution, then what do you do?

Use the central limit theorem

When can a sampling distribution of p be approximated by a normal distribution?

Whenever np >= 5 and n(1-P)>= 5

judgement sampling

a non-probability method of sampling whereby elements are selected for the sample based on the judgement of the person doing the study

convenience sampling

a non-probability method of sampling whereby elements are selected for the sample on the basis of convenience

cluster sampling

a probability sampling method in which the population is first divided into clusters and then a simple random sample of the clusters is taken

Stratified random sampling

a probability sampling method in which the population is first divided into strata and a simple random sample is then taken from each stratum

systematic sampling

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

Simple Random Sample (finite population)

a sample size n from a finite population of size N is a sample selected such that each possible sample of size n has the same probability of being selected

Function that shows the number of different simple random samples of size n that can be selected from a finite population of size N is...

combination function

Would this be a sampling from a finite or infinite population: Obtain a sample of cars crossing the golden gate bridge on a typical weekday?

infinite

If the population you are selecting a random sample from has a normal distribution, then what is the distribution of the sample?

it has a normal distribution

sampling with replacement

once an element has been included in the sample it is returned to the population so that a previously selected element can be selected again and therefore may appear in the sample more than once.

sampling without replacement

once an element has been included in the sample, it is removed from the population and cannot be selected a second time

When trying to find the probability that the sample mean will fall within x of the population mean, what function do you use?

standard normal distribution

Expression to compute the standard deviation of a sampling distribution

std. deviation of the population/square root of n

standard error

the standard deviation of a point estimator

Standard Error of the mean

the standard deviation of the sample mean

A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the x is used to estimate u. What is the probability that the sample mean will be within +/- 5 of the population mean?

use the function =normdist(x,mean,std. dev, true) to find the probability of 205 and 195, and subtract them from one-another =.6826 *may need to find the std. deviation for the sample first

When is a point estimator consistent?

when a property of a point estimator that is present whenever larger samples sizes tend to provide point estimates closer to the population parameter

Random Sample of infinite population

when sampling a population but the population is infinitely large or the elements of the population are being generated by an ongoing process for which there is no limit on the number of elements that can be generated.

Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 2 can be selected. What is the probability that each same of size 2 is selected?

with 10 samples, each has a probability of 1/10

Is the sample mean more efficient than the sample median?

yes