The topic is: Modelling the temperature each week of various citiesAttached is the IA checklist, the official criteria sheet and an example of work.
ibmath_mathstudies-SP-ch02.indd Sample project 2© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute 1 Sample project2 This Maths Studies project has been graded by a moderator. As you read through it, you will see comments from the moderator in boxes like this: At the end of the sample project is a summary of the moderator’s grades, showing how the project has been graded against all the criteria A to G. These criteria are explained in detail in chapter 13 of the Mathematical Studies textbook. Reading projects and the moderator’s comments will help you to see where marks are gained and lost, and will give you helpful tips in writing your own project. Is lung capacity affected by smoking, sport, height or gender Table of contents Introduction page 2 Data page 3 Mean page 4 Standard deviation page 5 Mean lung capacity page 7 Scatter graph, r page 7 χ2 Test page 8 Validity and conclusion page 9 Raw data page 11 Moderator’s comment: The project has a title Moderator’s comment: Sample project 2© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute 2 Introduction Aim of the project: This project is aimed to fi gure out if smoking, sport, gender or height infl uences lung capacity. In order to fi gure out what infl uences the lung capacity, data will be collected and analyzed. Comparisons between chosen smokers and non-smokers will be carried out in order to see whether smoking infl uences the lung capacity. It is expected that general lung capacity is going to be bigger for non-smokers and smaller for smokers, male and female, thus it is the aim of the project and will be investigated through analysis of data. 1 To check if this hypothesis is true, measuring lung capacity procedure will take place. 2 I wanted to test 40 individuals, divided into female and male groups, smokers and non smoker. (10 male smokers, 10 male non-smokers, 10 female smokers, 10 female non-smokers). So I picked students at random from the IB diploma programme in my school and asked if they were smokers or non smokers. Once I had 10 of each gender that were smokers and 10 that were non smokers I asked them to complete the questionnaire and then started the test that would measure their lung capacity. 3 Age from 16 till 21 years old because 16 is the legal age for smoking in the Netherlands. 4 Every person gets 3 tries to blow in the lung capacity meter so the average value can be picked. The type of questions asked: In order to investigate as it was mentioned before we need to collect and analyze the data. In order to do that, questionaires and forms are going to be composed for the 40 individuals that are tested for the lung capacity. Questionaires are going to contain these types of questions: 1 Gender? Male Female 2 Age? ..... 3 Are you an athlete? yes no The data taken from individuals that perform the lung capacity test. 1 Height 2 Lung capacity Hypotheses 1 Smoking decreases lung capacity 2 Lung volume depends on height, gender and also if the individual is an athlete. People who do sports have a higher lung volume which can be independent of height. Sample project 2© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute 3 3 Larger lung capacity expected to be: Smaller lung capacity expected to be: Males Females Non-smokers Smokers Athletes Non-athletes I will fi nd the mean lung capacity for each of the 40 participants and set up a table with the information collected. Each individual blows into the lung capacity meter three times and I will fi nd the mean of these three blows to use in my analysis. This gives me a more reliable reading than if the participant only blew once into the meter. I will compare the means of the lung capacities for each of the groups in order to fi nd out which group has the largest lung capacity and which one the smallest. I will also fi nd the standard deviation as this may be useful when deciding on the groupings for the chi-squared test to see if lung capacity is independent of gender or of smoking. I will also compare the mean lung capacity of athletes and non-athletes to fi nd out if athletes have larger lung capacities than non-athletes and I will draw a scatter diagram to fi nd out if there is any correlation between height and lung capacity. If it appears that there is a correlation then I will fi nd the correlation coeffi cient and possibly the equation of the regression line if the correlation coeffi cient is moderate to strong. Data See Appendix for raw data. Lung capacity data was collected with a Spirometer. Smoker females Age: 16 16 16 17 17 17 18 19 20 20 Height: 166 cm 170 cm 165 cm 161 cm 171 cm 164 cm 175 cm 165 cm 170 cm 165 cm Lung capacity: 2500 cc 2500 cc 2200 cc 2600 cc 2800 cc 2200 cc 2500 cc 2600 cc 2800 cc 2800 cc Athlete: No Yes No Yes No Yes No Yes No Yes Non – smoker females Age: 17 17 17 17 18 18 18 19 19 19 Height: 170 cm 160 cm 178 cm 156 cm 171 cm 163 cm 164 cm 175 cm 170 cm 163 cm Lung capacity: 3000 cc 2000 cc 3000 cc 2500 cc 3100 cc 2900 cc 2000 cc 2600 cc 2900 cc 2700 cc Athlete: No No No No No Yes No Yes No Yes Moderator’s comment: The project has a title, a task and a fairly detailed plan that is followed. Moderator’s comment: The raw data is relevant, suffi cient in quality but not in quantity and is set up for use. Sample project 2© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute 4 Smoker males Age: 17 17 18 18 18 18 19 19 19 20 Height: 185 cm 173 cm 183 cm 182 cm 175 cm 189 cm 187 cm 186 cm 177 cm 185 cm Lung capacity: 3300 cc 3300 cc 4000 cc 3900 cc 4000 cc 4000 cc 3500 cc 4600 cc 3500 cc 4100 cc Athlete: Yes Yes Yes Yes No No Yes Yes No Yes Non – smoker males Age: 16 16 16 16 17 17 18 18 18 18 Height: 179 cm 172 cm 171 cm 175 cm 176 cm 178 cm 175 cm 179 cm 180 cm 176 cm Lung capacity: 4200 cc 3100 cc 3500 cc 4100 cc 3100 cc 3800 cc 4400 cc 3500 cc 2600 cc 4000 cc Athlete: Yes Yes No Yes No No No Yes No Yes Hypothesis: Female Non-smokers should have less lung capacity than Male Non-smokers while Female Smokers should also have less lung capacity compared to Male Smokers. Generaly it is expected that lung capacity diff ers in gender, because females generally have smaller lungs. Calculating the means Non Smoker Females Lung capacity: ( 2000, 2000, 2500, 2600, (2700, 2900), 2900, 3000, 3000, 3100) Mean: 2000 2000 2500 2500 2600 2700 2900 2900 3000 3000 3100 10 + + + + + + + + + +( ) == =2670010 2670cc Smoker females Lung capacity: (2200, 2200, 2500, 2500, (2500, 2600), 2600, 2800, 2800, 2800) Mean: 2200 2200 2500 2500 2500 2600 2600 2800 2800 2800 10 2550+ + + + + + + + +( ) = 0010 2550= cc Non- smoker males Lung capacity: (2600, 3100, 3100, 3500, (3500, 3800), 4000, 4100, 4200, 4400) Mean: ( )2600 3100 3100 3500 3500 3800 4000 4100 4200 4400 10 3630+ + + + + + + + + = 0010 3630= cc Smoker males Lung capacity: (3300, 3300, 3500, 3500, 3900, 4000, 4000, 4000, 4100, 4600) Mean: ( )3300 3300 3500 3500 3900 4000 4000 4000 4100 4600 10 3820+ + + + + + + + + = 0010 3820= cc These values confi rm that males have larger lung capacity than females and female non-smokers have larger lung capacity than female smokers. However, male smokers have larger lung capacity than male non-smokers. This was an unexpected result but could be explained by the fact that there were more males who played sport and were smokers than non-smokers. Moderator’s comment: Simple process Sample project 2© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute 5 Standard deviation The standard deviation is going to be calculated to fi nd out how close the data is to the mean in each case. I will take the standard deviation into account when deciding on the groupings for the lung capacity in the chi-squared test. Process: Find the deviation of each entry from the mean, then square these values. Next fi nd the mean of the squared values and take the square root of this answer. Non – smoker females lung capacity Mean: 2670 Standard deviation xi xi – mean (xi – mean) 2 2000 (−670) 448900 2000 (−670) 448900 2500 (−170) 28900 2600 (−70 ) 4900 2700 30 900 2900 230 52900 2900 230 52900 3000 330 108900 3000 330 108900 3100 430 184900 Total: 1441000 SD: 1441000 10 380= Non – smoker males lung capacity: Mean: 3630 cc Standard deviation Xi Xi – mean (Xi – mean) 2 2600 (−1030) 1060900 3100 (−530) 280900 3100 (−530) 280900 3500 (−130) 16900 3500 (−130) 16900 3800 170 28900 4000 370 136900 4100 470 220900 4200 570 324900 4400 770 592900 Total: 2961000 SD: 2961000 10 =544 Moderator’s comment: Simple process Sample project 2© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute 6 Smoker females lung capacity: Mean: 2550 cc Standard deviation Xi Xi – mean (Xi – mean) 2 2200 (−350) 122500 2200 (−350) 122500 2500 (−50) 2500 2500 (−50) 2500 2500 (−50) 2500 2600 50 2500 2600 50 2500 2800 250 62500 2800 250 62500 2800 250 62500 Total: 445000 SD: 445000 10 = 211 Smoker male lung capacity: Mean: 3820 cc Standard deviation Xi Xi – mean (Xi – mean) 2 3300 −520 270400 3300 −520 270400 3500 −320 102400 3500 −320 −102400 3900 80 6400 4000 180 32400 4000 180 32400 4000 180 32400 4100 280 78400 4600 780 608400 Total: 1503600 SD: 1503600 10 = 392 Female Non-smoker Female Smoker Male Non-smoker Male Smoker Mean lung capacity 2670 2550 3630 3820 Standard deviation of lung capacity 380 211 544 392 The standard deviations shows that male non-smokers have the largest spread of data from the mean and female smoker’s