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Download 90288 – Select a Sample and make inferences - Mr-Kuijpers-Math
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90288 – Select a Sample and Make Inferences from Data The Mayor’s Claim 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. Listing the data gathered Include all information given for the population members (incl. list numbers) District 2000 2002 Increase District 2000 2002 Increase Appleton 279000 303000 24000 Central 202000 195000 -7000 Appleton 299000 326000 27000 Central 201000 195000 -6000 Appleton 285000 315000 30000 Central 134000 129000 -5000 Beachhead 141000 152000 11000 Central 214000 208000 -6000 Beachhead 141000 148000 7000 Central 132000 127000 -5000 Beachhead 127000 135000 8000 Central 179000 174000 -5000 Beachhead 182000 191000 9000 Central 214000 208000 -6000 Beachhead 140000 151000 11000 Central 129000 124000 -5000 Beachhead 236000 246000 10000 Central 146000 141000 -5000 Beachhead 192000 200000 8000 Central 121000 118000 -3000 Beachhead 167000 179000 12000 Central 217000 210000 -7000 Beachhead 203000 212000 9000 Central 136000 131000 -5000 Central 199000 193000 -6000 Darby 100000 108000 8000 Central 223000 216000 -7000 Darby 87000 93000 6000 Central 129000 124000 -5000 Darby 145000 158000 13000 Calculating Statistics An average: e.g. Mean = $3267 It would also be wise to calculate the Median as well. A measure of spread e.g. Standard Deviation = $10780 Other statistics can be calculated but you should at least list the 3 above. 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. 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. 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. Because of this reason I believe that my sample averages would make accurate predictions for the population and therefore reject the mayor’s claim. My sample did contain a couple of high price increases from Appleton and if I was to ignore these values my sample mean would most likely be even lower. To be totally sure of my prediction however, it may have been an idea to use the median for my prediction as this would not have been influenced by extreme values. 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.
