AP Statistics!!! Chapter 4 Review. Review of Chapter 4 Vocab Voluntary Response Sample ◦Participants ‘choose’ or volunteer themselves (not random; very.

AP Statistics!!!Chapter 4 Review

Review of Chapter 4 Vocab

Voluntary Response Sample◦ Participants ‘choose’ or volunteer themselves (not random; very biased)

Convenience Sample◦ We only include who is ‘convenient’ to survey. (not truly random; biased)

Simple Random Sample (SRS)◦ Every person has an equal chance to be selected (“all the names are in ‘one pot’”)

DO NOT BREAK INTO GROUPS!!! Stratified Random Sample

◦ Population is divided into groups or ‘strata’ that are made up of similar individuals within each group. You do an SRS within each group.

Systematic Sample◦ We sample every ‘kth’ person after the first person is randomly selected.

Multi-Stage Sample◦ Done on a large scale; combining other types of sampling methods; you sample to

choose GROUPS, then sample within the groups. Cluster Sample

◦ Population is divided into groups that don’t necessarily all look alike; the clusters should ‘mirror the population; you sample to choose GROUPS, then take a census within the group.

Sampling Error ◦Occurs in the act of choosing the sample

◦Undercoverage – certain members of population are ‘left out’

Non Sampling Error◦Occurs after sample is chosen

◦Non response – cannot be surveyed or refuse to answer question.

◦Response Bias ◦Poorly Worded Questions

Stratified Sampling: One type of sampling is called stratified sampling. Groups or classes inside a population that share a common characteristic are called strata. Example: In the population of all undergraduate college students, some strata might be freshman, sophomores, juniors, or seniors. Other strata might be men or women or in-state students or out-of-state students, and so on. In this method, the population if divided into at least two distinct strata. Then a (simple) random sample (SRS) of a certain size is drawn from each stratum.

Systematic Sampling: This is another popular method of sampling. In this method, it is assumed that the elements of the population are arranged in some natural sequential order. Then we select a (random) starting point and select every kth element for our sample. For example, to obtain a systematic sample of 20 students going through the cafeteria line at lunch, we could pick a random number between, say 0 and 10.

Cluster Sampling: Cluster sampling is a method used extensively by government agencies and certain private research organizations. In cluster sampling we begin by dividing the demographic area into sections. Then we randomly select the sections or clusters. Depending on the size of the cluster, every member of the cluster or a random sample of members of the cluster is included in the sample. For example, in conducting a survey of school children in a large city, we could first randomly select 30 schools and then include all the children from each school or a random sample of children from each school.

Convenience Sampling: This type of sampling simply uses results or data that are conveniently and readily obtained. In some cases, this may be all that is available, and in many cases, it is better than no information at all. However, convenience sampling does run the risk of being severely biased. For instance, consider a newsperson who wishes to get the ‘opinions of the people’ about a proposed seat tax to be imposed on tickets to all sporting events. The revenues from the seat tax will then be used to support the local symphony. The newsperson stands in front of a classical music store at noon and surveys the first five people coming out of the store who will cooperate. This method of choosing a sample will produce some opinions, and perhaps some human interest stories, but it certainly has bias.

Categorize the type of sampling method used in each of the following situations.

(simple random (SRS); stratified; systematic; cluster, multi-stage or convenience)◦To conduct a pre-election opinion poll on the latest

school board election, samples of 5 households from each telephone prefix (first three digits of the phone numbers) in the voting district were called.

 ANSWER: Multi-Stage

Categorize the type of sampling method used in each of the following situations.

(simple random (SRS); stratified; systematic; cluster, multi-stage or convenience)

To conduct a study on depression among the elderly, a sample of 30 patients in one nursing home was used.

ANSWER: Convenience

Categorize the type of sampling method used in each of the following situations.

(simple random (SRS); stratified; systematic; cluster, multi-stage or convenience)

Subscribers to the magazine Sound Alive were assigned numbers. Then a sample of 30 subscribers was selected by using a random number table. The subscribers in the sample were invited to rate new compact disc players for a “What a Subscribers Think” column.

ANSWER: Simple Random (SRS)

Categorize the type of sampling method used in each of the following situations.

(simple random (SRS); stratified; systematic; cluster, multi-stage or convenience)

To maintain quality control in a brewery, every 20th bottle of beer coming off the production line was opened and tested.

ANSWER: Systematic

Categorize the type of sampling method used in each of the following situations.

(simple random (SRS); stratified; systematic; cluster, multi-stage or convenience)

To judge the appeal of a proposed television sitcom, a random sample of 10 people from each of three different age categories were selected and those chose were asked to rate a pilot show.

ANSWER: Stratified

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below: Categorize each technique as:

(simple random sample, stratified sample, multi-stage, systematic sample, cluster sample, or convenience sample). ◦ Obtain a list of patients discharged from all MMH facilities. Divide

the patients according to length of hospital stay (3 days or less, 3-7 days, 8-14 days, more than 14 days). Draw simple random samples from each group.

ANSWER: Stratified

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below: Categorize each technique as:

(simple random sample, stratified sample, multi-stage, systematic sample, cluster sample, or convenience sample).

Obtain lists of patients discharged from all MMH facilities. Number these patients, and then use a random number table to obtain the sample.

ANSWER: Simple Random (SRS)

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below: Categorize each technique as:

(simple random sample, stratified sample, multi-stage, systematic sample, cluster sample, or convenience sample).

Randomly select some MMH facilities from each of five geographic regions, and then take random samples from each of these hospital discharge lists.

ANSWER: Multi-Stage

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below: Categorize each technique as:

(simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample).

At the beginning of the year, instruct each MMH facility to survey every 500th patient discharged.

ANSWER: Systematic

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below: Categorize each technique as:

(simple random sample, stratified sample, multi-stage, systematic sample, cluster sample, or convenience sample).

Randomly selected some MMH facilities and from each of the facilities, ask every person from a discharge list their satisfaction level.

ANSWER: Cluster Sample

Modern Managed Hospitals (MMH) is a national for-profit chain of hospitals. Management wants to survey patients discharged this past year to obtain patient satisfaction profiles. They wish to use a sample of such patients. Several sampling techniques are described below: Categorize each technique as:

(simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample).

Instruct each MMH facility to survey 10 discharged patients this week and send in the results.

ANSWER: Convenience

An important part of employee compensation is a benefits package that might include health insurance, life insurance, child car, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefit packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as: (simple random (SRS); stratified, systematic, cluster, multi-stage, or convenience).◦ Assign each business in the Island Business Directory a number

and then use a random number table to select the businesses to be included in the sample.

ANSWER: Simple Random (SRS)

An important part of employee compensation is a benefits package that might include health insurance, life insurance, child car, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefit packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as: (simple random (SRS); stratified, systematic, cluster, multi-stage, or convenience).

Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block or building and interview an employee from each business found. Each researcher can have the rest of the day off after getting responses from 20 different businesses.

ANSWER: Convenience

An important part of employee compensation is a benefits package that might include health insurance, life insurance, child car, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefit packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as: (simple random (SRS); stratified, systematic, cluster, multi-stage, or convenience).

Use the postal ZIP Codes to divide the state into regions. Pick a random sample of 10 ZIP Codes areas and then pick a random sample of 10 businesses in each ZIP Code area.

ANSWER: Multi-Stage

An important part of employee compensation is a benefits package that might include health insurance, life insurance, child car, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefit packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as: (simple random (SRS); stratified, systematic, cluster, multi-stage, or convenience).

Use the Island Business Directory. Number all the businesses. Select a stating place at random, and then use every 50th business listed until you have 100 businesses.

ANSWER: Systematic

An important part of employee compensation is a benefits package that might include health insurance, life insurance, child car, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefit packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as: (simple random (SRS); stratified, systematic, cluster, multi-stage, or convenience).

Group the businesses according to type: medical, shipping, retain, manufacturing, financial, construction, restaurant, hotel, tourism, other. Then select a random sample of 10 businesses from each business type.

ANSWER: Stratified

An important part of employee compensation is a benefits package that might include health insurance, life insurance, child car, vacation days, retirement plan, parental leave, bonuses, etc. Suppose you want to conduct a survey of benefit packages available in private businesses in Hawaii. You want a sample size of 100. Some sampling techniques are described below. Categorize each technique as: (simple random (SRS); stratified, systematic, cluster, multi-stage, or convenience).

You randomly selected several city blocks and survey EVERY business located within that city block

ANSWER: Cluster

FRAPPY #1: ‘DORM FOOD’

At a certain university, students who live in dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food service there. The dining hall manager decides to do a survey to estimate the proportion of students living in the dormitories who think the quality of food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question:

Many students believe that the food served in the dining hall needs improvement. Do you think that the quality of food services here needs improvement, even though that would increase the cost of the meal plan?

_____ Yes _____ No ______ No Opinion.

Questions…

a. In this setting, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias.

b. In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias.

SCORING CRITERIA & INTENT

INTENT: Measures student knowledge of: ◦ How bias affects sample selection.◦ How wording of question affects sample results.

Scoring Criteria: ◦ Part a:

Must correctly explain how this type of sampling method will introduce bias.

Must create a better sampling method that would avoid/lessen bias.

◦ Part b: Must explain how the wording of the question introduced

bias. Must offer a better way to word the question.

Model Solution

Part a: ◦ The issue is that the first 100 people who enter the dining

hall are likely individuals who like the food the most, simply because they are there and are FIRST to be in line.

◦ ANSWERS must show a better design (RANDOM); but should not simply resort to a census or a ‘better’ convenience sample. “I would have a dining hall employee hand a survey to every

10th person who is line all day long and ask them to answer the question.”

“I would do a stratified sample of all the dorms on campus. Within each dorm randomly select rooms based on their assigned room number and ask them the question.”

Model Solution

Part b: ◦TWO WAYS OF LOOKING AT IT…

The question is a ‘leading question’ in that it suggests that other students have already expressed there disapproval of the food in the dining hall, which would make students chooses ‘yes’

The question also suggest rising costs of the meal plan, which would cause students to answer ‘no’

◦BETTER WAY: “It would be best to leave out the part stating how other

students feel and the part about the increase in costs and just ask: “Do you think the quality of food services here needs improvement?”

AP Statistics – Chapter 4 FRAPPY Practice #42011 AP Statistics Exam Question #3

An apartment building has nine floors and each floor has four apartments. The building owner wants to install new carpeting in eight apartments to see how well it wears before she decides whether to replace the carpet in the entire building.

The figure below shows the floors of apartments in the building with their apartment numbers. Only the nine apartments indicated with an asterisk (*) have children in the apartment.

a. For convenience, the apartment building owner wants to use a cluster sampling method, in which the floors are clusters, to select the eight apartments. Describe a process for randomly selecting eight different apartments using this method.  b. An alternative sampling method would be to select a stratified random sample of eight apartments, where the strata are apartments with children and apartments with no children. A stratified random sample of size eight might include two randomly selected apartments with children and six randomly selected apartments with no children. In the context of this situation, give one statistical advantage of selecting such a stratified sample as opposed to a cluster sample of eight apartments using the floors as clusters.