1. 90288 – Select a Sample and Make Inferences from Data The Mayor’s Claim

2. Choosing a Sampling Method I am going to use a Stratified Sampling Method 1. Firstly I will stratify the population into districts and number them accordingly. Central 1-100, Darby 1-20, Appleton 1-20 and Beachhead 1-60 2. To calculate the right proportion of districts for my sample I will use: Number in district x 30 i.e. 100 x 30 = 15 Total in population 200 I will need 15 Central, 3 Darby, 3 Appleton and 9 Beachhead houses 3. To pick my sample I will use the random number on my calculator. I will use the formula: 100Ran#+1 to pick the 15 from Central, 20Ran#+1 to pick 3 from Darby etc 4. I will ignore any repeats and numbers after the decimal point (important to include this) 5. I will relate the random numbers back to the population to pick the 30 houses for my sample. 6. I will then calculate the appropriate statistics to reject/accept the mayor’s claim.

3. Listing the data gathered Include all information given for the population members (incl. list numbers) District20002002IncreaseDistrict20002002Increase Appleton27900030300024000Central202000195000-7000 Appleton29900032600027000Central201000195000-6000 Appleton28500031500030000Central134000129000-5000 Beachhead14100015200011000Central214000208000-6000 Beachhead1410001480007000Central132000127000-5000 Beachhead1270001350008000Central179000174000-5000 Beachhead1820001910009000Central214000208000-6000 Beachhead14000015100011000Central129000124000-5000 Beachhead23600024600010000Central146000141000-5000 Beachhead1920002000008000Central121000118000-3000 Beachhead16700017900012000Central217000210000-7000 Beachhead2030002120009000Central136000131000-5000 Central199000193000-6000Darby1000001080008000 Central223000216000-7000Darby87000930006000 Central129000124000-5000Darby14500015800013000

4. Calculating Statistics An average: e.g. Mean = $3667 It would also be wise to calculate the Median as well. e.g Median = $1500 A measure of spread e.g. Standard Deviation = $10780 Other statistics can be calculated but you should at least list the 3 above.

5. Making an Inference Remember the key words to use in your inference: e.g. I predict the population mean house price increase to be approximately $3300 Then make sure if you have answered the actual problem e.g. From my prediction, I believe that the Mayor’s claim was too high.

6. Justifying Choice of Sampling Method It is best to justify the use of the Stratified Sampling Method e.g. I have chosen this method as I have noticed that there are different numbers of houses (proportions) in each district. Using stratified sampling will enable me to obtain the correct proportion of all four districts into my sample. I will also be selecting the houses by random sampling so every house still has an equal chance of being selected. This should give me a sample that is representative of the population and is not bias.

7. Is the Sample Representative? Remember it is OK if you don’t think your sample is representative! e.g. I think that the sample I have chosen is representative of the population. Each of the four districts are fairly represented in the correct proportions and within each district I have a good range of house prices.

8. Justify Your Inference This could be justifying the statistic you used (i.e. mean or median). You could either justify using the standard deviation or by drawing a box and whisker plot e.g. As the standard deviation calculated for my sample was high, the actual sample obtained would be considered to be quite varied. Therefore the sample mean would probably not be the best average to use. The make a better prediction, I probably should have used the median as the average. Or: The box and whisker plot (you should actually draw it) of my sample shows it to be slightly skewed. This would indicate that the mean for the sample would not be the best average to use for the estimate. As such, to make a better prediction I could have used the median. You will notice from the sample statistics that the median of $1500 is well below the mean of $3667 indicating that the sample did contain some extreme values. (another way to justify is to compare your mean and median). Therefore the median would have been the best statistic to use and further reject the Mayors claim.

9. Evaluating Your Processes Improving your Sampling Method Limitations of your sampling and statistical processes Limitations of your conclusion Accuracy or appropriateness of your estimate Distribution of the data It is always worthwhile to look to discuss way to improve things as it is unlikely your methods used were perfect. It is ok to say you could’ve done things better. Remember to always write more statements than that required.