Hypothesis Testing

Background A study has been carried out investigating weight loss for amateur athletes across Ireland when individuals are following a high protein diet.' A random sample of 26 athletes have been enrolled in the study and various other measurements have been taken. The researchers record the athlete's weight before the study begins and then the athletes are randomly allocated to new high protein diet and a control group. After 6 weeks, the weights are then recorded and the researchers want to find out if there's any difference in weight loss between the two groups. In addition, they have collected all this extra data and your job is to answer some questions they have regarding this extra information. The following table shows all the variables you have in your data set and a short description of each of them. Variable Description AthleteID Athlete identification number Age (in years) Sex of athlete (Male/Female) Height Height (in cm) Weight1 Weight before the study (in kg) Weight2 Weight after the study (in kg) BMI Body Mass Index of athelete before the study (in kg/m) Sprint 100 100m sprint time in seconds) Sprint400 400m sprint time in seconds) Distance What distance the runner prefers (Short/Long/Sprint) Gym Does the athlete regularly lift weights (Yes/No) Diet Diet preference (None, Vegetarian or Vegan) StudyGroup What diet group the athlete belongs to (Control/Diet) Age Sex Hypothesis Testing Now, the researchers want to compare differences between groups. Please use appropriate significance levels. In all cases you must report the critical value and the p-value. When appropriate, analysis should include a confidence interval to report results. 1. The average BMI of people in Ireland who class themselves as fit have a BMI of 23.5. Does theis data suggest that amateur athletes have an equal BMI to this? 2. Is there a difference in the 100m sprint times between athletes who regularly lift weights and athletes who don't? 3. Carry out an appropriate test to investigate if there was any weight loss in all the athletes after the six week period. What type of test is this? 4. Do the data suggest that the new diet intervention reduces the athlete's weight? 5. Is there a relationship between training in the gym regularly and average BMI? 6. Do the data provide evidence to indicate that the athlete's weight training is dependent on the athlete's diet? 7. It is estimated in Ireland that 50% of individuals have no diet preference, 35% of individuals now identify as vegeatarian and 15% are now vegan. Do these athletes follow the same diet distribution as the Irish population? 8. Is there a difference in 400m sprint times between males and females? What type of error could you have made in this test? With what probability could you have made this error? AthleteID Age Sex Height Weight Weight2 BMI Sprint100 Sprint400 Distance Gym Diet Study Group 1 250 31 Female 157.71 54.47 54.5 21.9 14.1 70.5 Long Y Vegan Diet 2 251 16 Female 161.59 56.92 57 21.8 12.8 69.2 Short N None Control 3 252 15 Male 178.23 63.53 63.6 20 11.9 63.4 Long N None Control 4 253 18 Male 180.93 73.66 71.9 22.5 11.5 59.8 Short N None Diet 5 254 28 Female 163.15 55.1 54.1 20.7 13.7 68.8 Sprint Y Vegetarian Diet 6 255 29 Male 176.59 63.93 63.4 20.5 11.1 59.7 Sprint Y Vegetarian Control 7 256 25 Female 166.09 65.38 66.9 23.7 13.3 70.9 Sprint Y Vegan Control 257 39 Male 182.33 74.8 74.1 22.5 11 64.5 Short N None Diet 258 32 Female 158.03 56.44 56.2 22.6 14 73.4 Short N None Diet 10 259 16 Female 164.28 65.31 64.2 24.2 13.2 66.5 Short Y Vegetarian Control 11 260 34 Female 169.37 64.26 63.4 22.4 14.3 79.1 Short Y None Diet 12 261 22 Male 182.1 78.59 75.9 23.7 11.2 63.2 Short N Vegan Diet 13 262 35 Male 181.34 69.39 68.7 21.1 11.4 59.8 Short N Vegetarian Diet 14 263 40 Female 159.77 64.33 64.2 25.2 13.9 69.7 Sprint N None Control 15 264 29 Male 181.47 68.17 67.9 20.7 10.6 58.7 Long Y Vegetarian Control 16 265 27 Male 176.56 58.61 58.9 18.8 11 55.9 Sprint Y None Control 17 266 22 Male 176.43 61.63 61.3 19.8 11.9 66.2 Sprint Y None Control 18 267 18 Male 178.12 78.05 76.7 24.6 10.5 55.4 Sprint N None Diet 19 268 24 Male 183.36 76.66 76.1 22.8 10.9 64.5 Sprint Y None Diet 20 269 19 Male 177.14 58.36 58.2 18.6 10.6 58.9 Short Y Vegan Control 21 270 29 Male 173.19 75.59 74.6 25.2 10.5 54.7 Long Y Vegan Diet 22 271 22 Male 176.83 69.42 69.5 22.2 11.9 64.9 Short Y Vegetarian Control 23 272 35 Male 167.38 50.99 49.7 18.2 10.4 58.2 Long Y Vegan Diet 24 273 27 Female 152.6 45.64 45.7 19.6 12.7 66.2 Long N Vegan Control 25 274 23 Male 167.63 50.86 50.4 18.1 11.3 57.3 Sprint N Vegetarian Control 26 275 36 Female 159.93 53.97 53.3 21.1 13.2 69.7 Sprint Y Vegetarian Diet