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2. Refresh Test the questionnaire on a few people first to see if it works OK or needs amending. Pilot survey: Sample Size and Type: Decide on the size and type of the sample that you intend to use. Will it be a simple random sample or a stratified random sample? Simple Random Sampling After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample.

3. Samples and Populations. In our earlier work on surveys we produced questionnaires to be given out to students in a school. The number of students in the school is called the population and the number of students that receive the questionnaire is called the sample. However, in statistics the word population has a much broader meaning and can be taken to be a group of anything (for example objects as well as people). The sample is that part of the population under consideration. For instance the population could be the number of light bulbs produced by a manufacture during a day and the sample could be every 50 th light bulb produced. Samples are taken by manufacturers of products to ensure that the quality is up to the required standard.

4. Population Possible Samples TV’s produced by a factory..Every 20 th TV Children’s trousers made in a factory.Every 30 th pair Punctuality of buses in a city. Check punctuality for 10 different routes Tyre produced by manufacturer.5% of all tyres produced

5. Why do we take a Sample? Simple Random Sampling Too expensive and too time consuming to survey an entire population. If the population under consideration is a set of objects such as car tyres/nuts and bolts etc then they may need to be tested to destruction. After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample.

6. Precautions with the Sample Simple Random Sampling The sample taken should be representative of the whole population under consideration. A sample that is not representative is said to be biased. After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample.

7. Simple Random Sampling Discuss why the following samples may not be representative (i.e. biased) of the populations. 1. Stuart’s group are going to carry out a survey about the average time spent on homework by students in their school. They decide to give a questionnaire about this to every one in their class 2. Sara’s group are going to carry out a survey about peoples views on reading books and whether this improves spelling standards. They decide to sample the views of students as they enter the library. 3. A retail outlet wants to get views on what people think about digital TV’s. They decide to ring up the first fifty people in the phone book. 4. A car manufacture wants to check the quality of doors made for its cars by one of their five “door teams” (teams A,B,C,D and E) in the factory. It decides to check 10% of all doors made by team B on a Friday afternoon.

8. Simple Random Sampling In a simple random sample every member of the population under consideration has an equal chance of being chosen. After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample. We will look at the methods of simple random sampling in the context of a school survey on homework.

9. Hat Simple Random Sampling 324 538 214 43 Method 1 Example: Out of a school of 618 students forty are to be selected to take part in a survey on Homework. 1. Assign a three digit number from 001 to 618 to each student. 2. Write each number on a piece of paper (or use raffle tickets), place in a hat and mix up. 3. Draw the forty numbers from the hat.

10. Random Number Table Simple Random Sampling Method 2 2302630381679640598430036717423594127487 2319096605401936471686526327265424503435 3932733641909669021808356230672306278974 5515540320755395209419341065104182918317 3875866855608407259324376376180478034101 2980863442457146627642529518247407972710 057423 52341213905085288946376336874835 5589751436585619517734785517963569148831 1543810953143358693619016861358797090186 3930628660401903973412283373333720570884 0713220671601001414511086027984256745862 7814385473983309905102557275013982772790 0387019081590580471524312891 2564305463 4457690967139185832326523064842002565785 328142 50752926166378347931275596693264 3655182851785235707229046658895535623229 507402768617786406269327558451916128 55 0704459111560745879394752587326681711543 9542808356952363859425038824262746296435 0185456668415491564433345853817360796375 Use a random number table. You can start anywhere (i.e. randomly) in the table and go in any direction left, right, up or down in groups of 3 digits until all 40 numbers are chosen. In this example we start by going down then left. Starting from this 5 587 153 113092 570 254 915 644 333 Remove unwanted digits and continue until you have your 40 numbers.

11. Simple Random Sampling 2302630381679640598430036717423594127487 2319096605401936471686526327265424503435 3932733641909669021808356230672306278974 5515540320755395209419341065104182918317 3875866855608407259324376376180478034101 2980863442457146627642529518247407972710 057423 52341213905085288946376336874835 5589751436585619517734785517963569148831 1543810953143358693619016861358797090186 3930628660401903973412283373333720570884 0713220671601001414511086027984256745862 7814385473983309905102557275013982772790 0387019081590580471524312891 2564305463 4457690967139185832326523064842002565785 328142 50752926166378347931275596693264 3655182851785235707229046658895535623229 507402768617786406269327558451916128 55 0704459111560745879394752587326681711543 9542808356952363859425038824262746296435 0185456668415491564433345853817360796375 Use your printed random table to take a random sample of size 20 from a school population of 450.

12. Calculator Simple Random Sampling Method 3 Use a random number generator. Using a scientific calculator press Shift/Inv key followed by the RND/random key to generate three digit numbers from 0.001 to 0.999 0.3860.5250.0230.8740.7020.123 386525023874702123 Ignore the decimal points and simply read as a 3 digit number.

13. Simple Random Sampling 0.3860.5250.0230.8740.7020.123 386525023874702123 Ignore the decimal points and simply read as a 3 digit number. Use your calculator to obtain a random sample of size 25 from a school population of 580.

14. Worksheet 2302630381679640598430036717423594127487 2319096605401936471686526327265424503435 3932733641909669021808356230672306278974 5515540320755395209419341065104182918317 3875866855608407259324376376180478034101 2980863442457146627642529518247407972710 057423 52341213905085288946376336874835 5589751436585619517734785517963569148831 1543810953143358693619016861358797090186 3930628660401903973412283373333720570884 0713220671601001414511086027984256745862 7814385473983309905102557275013982772790 0387019081590580471524312891 2564305463 4457690967139185832326523064842002565785 328142 50752926166378347931275596693264 3655182851785235707229046658895535623229 507402768617786406269327558451916128 55 0704459111560745879394752587326681711543 9542808356952363859425038824262746296435 0185456668415491564433345853817360796375 Worksheet