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Ch. 4: Designing Studies SECTION 4. 1 – SAMPLES & SURVEYS, CONT.

How to Choose an SRS Choosing an SRS With Technology Step 1: Label. Give each individual in the population a distinct numerical label from 1 to N. Step 2: Randomize. Use a random number generator to obtain n different integers from 1 to N. How to Choose an SRS Using Table D Step 1: Label. Give each member of the population a numerical label with the same number of digits. Use as few digits as possible. Step 2: Randomize. Read consecutive groups of digits of the appropriate length from left to right across a line in Table D. Ignore any group of digits that wasn’t used as a label or that duplicates a label already in the sample. Stop when you have chosen n different labels. Your sample contains the individuals whose labels you find.

Example p. 217 Choosing an SRS with Table D The school newspaper is planning an article on family-friendly places to stay over spring break at a nearby beach town. The editors intend to call 4 randomly chosen hotels to ask about their amenities for families with children. They have an alphabetized list of all 28 hotels in the town. Use Table D at line 130 to choose an SRS of 4 hotels for the editors to call.

Example p. 217 Choosing an SRS with Table D 01 Aloha Kai 02 Anchor Down 03 Banana Bay 04 Banyan Tree 05 Beach Castle 06 Best Western 07 Cabana 69051 64817 08 Captiva 09 Casa del Mar 10 Coconuts 11 Diplomat 12 Holiday Inn 13 Lime Tree 14 Outrigger 87174 09517 15 Palm Tree 16 Radisson 17 Ramada 18 Sandpiper 19 Sea Castle 20 Sea Club 21 Sea Grape 84534 22 Sea Shell 23 Silver Beach 24 Sunset Beach 25 Tradewinds 26 Tropical Breeze 27 Tropical Shores 28 Veranda 06489 87201 97245 69 05 16 48 17 87 17 40 95 17 84 53 40 64 89 87 20 Our SRS of 4 hotels for the editors to contact is: 05 Beach Castle, 16 Radisson, 17 Ramada, and 20 Sea Club.

Stratified Random Sample To get a stratified random sample, start by classifying the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the sample.

Reminder �For an simple random sample (SRS), each individual and each group of n individuals must have an equal chance of being chosen.

SRS or Stratified? �Say I have a class of 32 students: 24 seniors and 8 juniors. I will randomly choose 8 students to survey to represent the class. SRS �What if I choose 6 of the 24 seniors randomly and 2 of the 8 juniors randomly to form my 8 students? Stratified Random Sample

Cluster Sample To get a cluster sample, start by classifying the population into groups of individuals that are located near each other, called clusters. Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample.

*Systematic Random Sample A systematic random sample is a sample drawn by selecting individuals systematically (every kth individual) from a sampling frame.

Check Your Understanding p. 223 The manager of a sports arena wants to learn more about the financial status of the people who are attending an NBA basketball game. He would like to give a survey to a representative sample of the more than 20, 000 fans in attendance. Ticket prices for the game vary a great deal: seats near the court cost over $100 each, while seats in the top rows of the arena cost $25 each. The arena is divided into 30 numbered sections, from 101 to 130. Each section has rows of seats labeled with letters from A (nearest the court) to ZZ (top row of the arena). 1. Explain why it might be difficult to give the survey to an SRS of 200 fans. It would be hard to identify 200 different seats and go to those seats in the arena. This might take a long time.

Check Your Understanding p. 223 The manager of a sports arena wants to learn more about the financial status of the people who are attending an NBA basketball game. He would like to give a survey to a representative sample of the more than 20, 000 fans in attendance. Ticket prices for the game vary a great deal: seats near the court cost over $100 each, while seats in the top rows of the arena cost $25 each. The arena is divided into 30 numbered sections, from 101 to 130. Each section has rows of seats labeled with letters from A (nearest the court) to ZZ (top row of the arena). 2. Which would be a better way to take a stratified random sample of fans: using the lettered rows or the numbered sections as strata? Explain. Best to create strata where people within a stratum are similar but different from people in other strata. Since the lettered rows are a certain distance from the court, each seat in a row should have about the same price.

Check Your Understanding p. 223 The manager of a sports arena wants to learn more about the financial status of the people who are attending an NBA basketball game. He would like to give a survey to a representative sample of the more than 20, 000 fans in attendance. Ticket prices for the game vary a great deal: seats near the court cost over $100 each, while seats in the top rows of the arena cost $25 each. The arena is divided into 30 numbered sections, from 101 to 130. Each section has rows of seats labeled with letters from A (nearest the court) to ZZ (top row of the arena). 3. Which would be a better way to take a cluster sample of fans: using the lettered rows or the numbered sections as clusters? Explain. Best if people in each cluster represent the variability found in the population. It would be better to use the numbered sections because they include different prices (has more variability).

Inference for Sampling The process of drawing conclusions about a population on the basis of sample data is called inference. Why should we rely on random sampling? 1. To avoid bias in selecting samples from the list of available individuals. 2. The laws of probability allow trustworthy inference about the population • Results from random samples come with a margin of error that sets bounds on the size of the likely error. • Larger random samples give better information about the population than smaller samples.

Sample Surveys: What Can Go Wrong? Types of Bias Undercoverage occurs when some members of the population cannot be chosen in a sample. Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to participate. A systematic pattern of incorrect responses in a sample survey leads to response bias. The wording of questions is the most important influence on the answers given to a sample survey.

Check Your Understanding p. 228 1. Each of the following is a possible source of bias in a sample survey. Name the type of bias that could result. a) b) c) The sample is chosen at random from a telephone directory. Undercoverage – some people may not have phones. Some people cannot be contacted in five calls. Nonresponse – can’t get a hold of people. Interviewers choose people walking by on the sidewalk to interview. Undercoverage – some people may be driving

Check Your Understanding p. 228 2. A survey paid for by makers of disposable diapers found that 84% of the sample opposed banning disposable diapers. Here is the actual question: It is estimated that disposable diapers account for less than 2% of the trash in today’s landfills. In contrast, beverage containers, third -class mail, and yard wastes are estimated to account for about 21% of the trash in landfills. Given this, in your opinion would it be fair to ban disposable diapers? Explain how the wording of the questions could result in bias. Be sure to specify the direction of the bias. They make it sound like disposable diapers are not that big of a problem, which will result in fewer people wanting to ban them.

What is this an example of? P. 227 Response Bias

Homework: Due Friday �P. 230 # 18, 19, 21, 23, 25, 29