Take Home Exam- Statistical Mania

This is your statistics take home exam. I expect everyone to do there own work without help from your classmates. Sharing this experience tends to prevent you or your classmate(s) from learning this material. To receive partial credit on a wrong answer. Show ALL YOUR WORK! This is worth 15% of your course grade. Good luck and let me know if you have any questions. This assignment is due 2/03/23

  1. What is the percent standard deviation (1,2,3) of 4,999 counts? Now calculate the %SD of all three. If 13,500 counts are added to 4,999 what happens to the SD and the %SD. If an image has 13,500 vs 4,999 what is the advantage of the image with greater counts?
  2. Define three types of errors and give an example of each which might occur in a nuclear medicine department. If applicable, indicate how you would prevent these errors from occurring.
    3. 13,232
    12,215
    13,213
    14,251
    12,254
    14,132
    12,254
    13,204
    12,245
  3. The above counts were collected from your well counts. Determine X.2
  4. From question 3, is the X2 value within the appropriate range? Discuss your results and relate this to the operation of your equipment based on the variation/randomness of decay.
  5. If the SD is 1317 and the mean is 81,475 counts, what is the CV?
  6. If you collect 55,414 counts from a 137Cs source, what is your percent error @ 2SD?
  7. How many counts does your thyroid need to be in order to only have a 1% error @ 3SD?
  8. What is the percent error of the following thyroid uptake at 2SDs? You must calculate the uptake first, to determine your answer. After you calculating the % uptake apply the % error. If a normal thyroid ranges between 10 to 30% uptake, then how confident are you with the results of this thyroid uptake?

  9. You have acquired a total of 12,115 counts in 5 minutes. What is the SD for this values at 68%, 95%, and 99%?
  10. Following a comparative analysis of Gated SPECT and planar imaging of the myocardium was assessed on a group of selected patients. All patients where then sent to cardiac cath for assessment (positive and negative).\
    11. Gated SPECT True False
    Positive 1141 68
    Negative 995 77
    		 
    Planar True False
    Positive 34 2
    Negative 25 1
    1. Calculate sensitivity, specificity, and accuracy
    2. Based on the above calculations define which method has a the better true positive/negative and false positive/negative rates in finding disease?
    3. Based on the patient population is there a concern of the data having inaccuracy?
  11. How many counts must a 128x128 matrix have if there was no more than a 1% error? Consider this at the pixel level that is applied to the entire acquired image.

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