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Simple Random Sampling After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample. Pilot survey: Test the questionnaire on a few people first to see if it works OK or needs amending. 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? Refresh

Simple Random Sampling 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 50th light bulb produced. Samples are taken by manufacturers of products to ensure that the quality is up to the required standard.

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

Simple Random Sampling After producing a questionnaire for your survey (see Questionnaires and Surveys) you will need to organise a sample. Why do we take a Sample? 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.

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

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.

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

Simple Random Sampling Method 1 214 43 538 324 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. Hat 3. Draw the forty numbers from the hat.

Simple Random Sampling Method 2 Simple Random Sampling 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. 23 02 63 03 81 67 96 40 59 84 30 17 42 35 94 12 74 87 19 09 66 05 36 47 16 86 52 27 26 54 24 50 34 39 32 73 41 90 69 18 08 62 06 89 55 15 20 75 53 95 10 65 82 91 83 38 68 60 07 25 93 37 76 04 78 01 29 80 45 71 46 97 13 85 28 48 14 58 56 51 77 88 31 43 33 61 57 22 11 98 72 64 44 79 70 Starting from this 5 587 153 113 092 570 254 915 644 Random Number Table 333 Remove unwanted digits and continue until you have your 40 numbers.

Simple Random Sampling Use your printed random table to take a random sample of size 20 from a school population of 450. 23 02 63 03 81 67 96 40 59 84 30 17 42 35 94 12 74 87 19 09 66 05 36 47 16 86 52 27 26 54 24 50 34 39 32 73 41 90 69 18 08 62 06 89 55 15 20 75 53 95 10 65 82 91 83 38 68 60 07 25 93 37 76 04 78 01 29 80 45 71 46 97 13 85 28 48 14 58 56 51 77 88 31 43 33 61 57 22 11 98 72 64 44 79 70

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 0.386 0.525 0.023 0.874 0.702 0.123 Ignore the decimal points and simply read as a 3 digit number. 386 525 023 874 702 123 Calculator

Simple Random Sampling Use your calculator to obtain a random sample of size 25 from a school population of 580. 0.386 0.525 0.023 0.874 0.702 0.123 Ignore the decimal points and simply read as a 3 digit number. 386 525 023 874 702 123

Worksheet 23 02 63 03 81 67 96 40 59 84 30 17 42 35 94 12 74 87 19 09 66 05 36 47 16 86 52 27 26 54 24 50 34 39 32 73 41 90 69 18 08 62 06 89 55 15 20 75 53 95 10 65 82 91 83 38 68 60 07 25 93 37 76 04 78 01 29 80 45 71 46 97 13 85 28 48 14 58 56 51 77 88 31 43 33 61 57 22 11 98 72 64 44 79 70 Worksheet