Stat 121 - Lesson 3

Officials of a major university want to know what percent of their students recycle paper. They randomly sample 200 students to find out. What is the sample?

The 200 students in the sample.

What is inference in statistics?

The process of drawing conclusions about a population on the basis of sample data. It's called this because we infer information about the population from what we know about the sample.

If individuals in a population are numbered from 1 to 50, what two random digits would lead you to select person number 8?

To make 8 at two digit number, you have to add a zero to the front and make it "08."

True or false: A random sample is required for valid inference.

True

True or false: All random samples require use of some type of random device, not human subjectivity.

True

True or false: If a sample is truly random, then it has a probability of being selected.

True

True or false: Inference is not appropriate using results from a non-random sample.

True

True or false: Stratified sampling can only be done if the population can be classified into groups according to some characteristic known prior to the survey.

True

What is statistical inference?

Using information from a sample to draw conclusions about a population.

What is under-coverage bias?

Under-coverage occurs when the listing of the population is incomplete with individuals who belong to the population left off the list.

Officials of a major university want to know what percent of their students recycle paper. They randomly sample 200 students to find out. Which of the following is an important question that should be asked?

A. How much does each student pay for rent? B. ****What exactly is a "student?" Are part-time, online and/or evening students included?**** C. How many credits is each student taking? D. What is the GPA of each student?

Officials of a major university want to know what percent of their students recycle paper. They randomly sample 200 students to find out. Which of the following is an important question that should be asked?

A. What exactly does "recycle paper" imply? B. How often does a student recycle paper? Always? Sometimes? Once is a rare while? C. How does a student recycle paper? D. ****All of the above.****

Officials of a major university want to know what percent of their students recycle paper. They randomly sample 200 students to find out. What is the population of interest?

All students at this major university.

What type of sample allows for invoking laws of probability to make inference, Non-random sample or random?

Because random samples use a random device to select individuals to be sampled, laws of probability can be applied to the results.

What type of sampling could have response bias, random or non-random?

Both types of sampling could have non-response or response bias.

Why use random samples?

Eliminates sampling bias, and invokes the laws of probability to make trustworthy inference about a population

True or false: If a sample is truly random, we cannot compute the probability of getting that sample.

False, If a sample is truly random, then we CAN compute the probability of getting that sample.

True or false: After taking a stratified sample, the results are analyzed separately for each group

False. After taking a stratified sample, the results from each strata are combined to form a complete sample.

True or false: Two samples, if taken at random, will give the same results.

False. Even if two samples are taken at random, the sample results will differ due to chance.

True or false: For stratified sampling, a simple random sample is taken from some of the stratum.

False. For stratified sampling, a simple random sample is taken from EVERY stratum.

True or false: Statistical inference is valid for all types of samples.

False. It is only valid for random samples

True or false: A good random sample always exactly mirrors the population from which it is taken.

False. It is unlikely that the results from a random sample are exactly the same as the population.

True or false: Bias is only possible in non-random samples

False. Non-response bias and response bias are both possible in random samples.

For a two-stage multistage sample, what sampling is done in the first stage?

For two stages, a sample of groups is taken in the first stage and then the individuals from within those groups in the second stage.

Which of the following is NOT a problem for a non-random sample? A. Harder to obtain than a random sample. B. Principles of chance cannot be applied. C. Almost always has bias. D. Has no theoretical base for making inference.

Harder to obtain than a random sample.

How does a stratified sample differ from a two-stage multistage sample?

In multistage sampling, groups are first sampled and then individuals are only sampled from those groups. But for stratified sampling, individuals are sampled from every group.

What is interviewer bias?

Interviewer bias is a special kind of response bias. It occurs when the interviewer influences the answers given by the respondent.

What is the benefit of choosing a sample by chance?

It eliminates favoritism by the sampler and self selection by respondents. It decreases bias by giving all individuals in population equal chance to be selected.

What is non-response bias?

Non-response refers to not getting a response from a sampled individual. This could be because they refuse to respond or the individual could not be contacted.

What is question wording bias?

Question wording bias occurs when the wording of the question influences the respondent to give certain answers.

Why is a random sample preferred over a non-random sample?

Random samples are required for statistical inference so that bias is minimal, probabilities can be computed and sampling error can be measured.

What type of sampling is required for valid inference?

Random sampling! Random sampling! Random SAMPLING!

What is respondent bias?

Respondent bias occurs whenever the respondent does not give correct answers to the questions. This bias could be due to lying, making up an answer because they don't know or forgot, misunderstanding the question, etc.

Response bias includes what 3 sub groups?

Respondent bias, interviewer bias, and questions wording bias

Freshmen students at a large university are required to live in the twenty university dorms. If fifty freshmen students are randomly selected from a list of all sampling, what type of sampling is this?

Simple random sample

If individuals in a population are numbered from 1 to 50, how many digits should you select each time from the random digit table?

Since 50 is a two digit number, you should select two digits each time.

If individuals in a population are numbered from 1 to 777, how many digits should you select each time from the random digit table?

Since 777 is a three digit number, you should select three digits each time.

Freshmen students at a large university are required to live in the twenty university dorms. If six dorms are randomly selected and then 12 freshmen students are randomly sampled from each of these six dorms, what type of sampling is this?

Since dorms are randomly selected in the first stage and freshmen are randomly selected from only those dorms in the second stage, this is multistage sampling.

Freshmen students at a large university are required to live in the twenty university dorms. If 15 freshman students are sampled from every dorm, what type of sampling is this?

Since freshmen are sampled from every dorm, this is stratified sampling.

Question 11. 1. Anna 5. Geoge 9. David 13. John 17. Tyler 2. Bryce 6.Tricia 10. Erica 14. Sharon 18. Jacob 3. Emily 7. Steven 11. Julie 15. Brooke 19. Joseph 4. Charles 8. Mark 12. Hannah 16. Elizabeth 20. Catherine Table 1.1 73196 69616 38312 39821 87358 10541 71970 39782 Table 1.2 A high school teacher wants to randomly select one of her students for a class presentation. She gives each student the numbers assigned in Table 1.1. Using the random numbers given in Table 1.2, starting from the left, who should she pick?

Since the students are labeled with two digits (#2 is 02), we have to use the random digits two at a time. 73 is not assigned, but 19 corresponds to Joseph.

For stratified sampling, the population is classified into groups prior to the survey. What are these groups called?

Strata

What type of bias is possible for a convenience sample of oranges from a truckload? Select all that apply.

When sampling oranges from a truckload, people are not involved, so only under-coverage bias is possible. In particular, oranges at the bottom of the truck are less likely to be sampled than oranges on the top.

Officials of a major university want to know what percent of their students recycle paper. They randomly sample 200 students to find out. What is the variable being measured on each student?

Whether student recycles paper.

What is a stratified random sample?

You first classify the population into groups of similar individuals (called strata). Then you choose a separate SRS in each stratum and combine these SRSs to form the full sample.

Explain why a stratified design can produce more precise information than an SRS of the same size:

by taking advantage of the fact that individuals in the same stratum are similar to one another.

SRS can be similar to...

drawing names out of a hat, where all names are completely equal in how likely they are to be selected

The first reason to rely on random sampling is to...

eliminate bias

For multistage sampling, when is a sample of individuals taken?

in the last stage

(larger or smaller) random samples give more accurate results than (larger or smaller) random samples

larger random sample is more accurate

Simple Random Sample (SRS) (definition)

of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected.

We do not allow __________ to select a sample to eliminate bias. Instead, random digit tables or computer software are used.

people

Fill in the blanks: Statistical inference is using information from a _______________ to draw conclusions about a ______________________.

sample, population

What is unique about a multistage sample?

samples are taken in stages

Say I was looking to gather data for an election and chose certain strata over a given state. How could I stratify the population?

separate people into Urban, suburban, and rural strata.