Math topic中文

Unbiased estimates of mean and variance

Use of unbiased estimates of the population mean and variance from a sample, including cases where the data are given in summarised form ∑x\sum x and ∑x2\sum x^2, or ∑(x−a)\sum(x-a) and ∑(x−a)2\sum(x-a)^2.

Practice questions

  1. 1A nutritionist claims that the mean number of calories in an energy bar is 350 cal. The nutritionist collected and measu…
  2. 2The owner of Eng Choo Farm claims that the eggs produced at his farm has an average cholesterol content of μ0\mu_0 mg pe…
  3. 3A bakery claims that the mass of a cake, on average, is 600 grams each. A random sample of 10 cakes is examined and the…
  4. 4An electrical appliance supplier is investigating the potential impact of monthly advertisement expenditure, denoted as…
  5. 5Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  6. 6Researchers at University S claimed that Fungus A, a strain of fungi that is typically found in soil and plants, was a…
  7. 7The waiting time for a patient to see a doctor in a clinic is TT minutes. The waiting times of a randomly chosen sample…
  8. 8Energy bars are a convenient source of nutrition for athletes. A typical energy bar weighs between 30-50 g and is likely…
  9. 9Section B: Probability and Statistics [35 marks] From past data, it is known that the mean time taken by students at…
  10. 10Korean dramas, or Kdramas, have been immensely popular among students, captivating their attention during leisure hours.…
  11. 11A farmer claims that the mean weight of the melons grown in his farm is at least 1.2 kg. A random sample of 10 melons is…
  12. 12The shear strength of soil is the ability of the soil to resist tensional stresses and sustain loads. The water content…
  13. 13Pat is invited to a game show. In the game, she is presented with a box with kk balls with either 1, 2, 3 or 4 printed…
  14. 14A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  15. 15A manufacturer claims that the mean lifetime of the light bulbs he produces is at least 1200 hours. A random sample of 1…
  16. 16Under normal continuous use, the average battery life of a PI-99 calculator is claimed to be kk hours. A random sample…
  17. 17Sharron who is an amateur swimmer has been attending swimming lessons. She records her time taken to swim 50 metres each…
  18. 18A company produces reinforcing bars for use in construction. The production manager claims that the mean tensile strengt…
  19. 19EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
  20. 20Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  21. 21The amount customers spend is often correlated with the amount of time they spend in stores. According to a national sur…
  22. 22A hand sanitiser company, Cleanser, claims that the mean volume of each bottle of their hand sanitiser is 15 ml. The con…
  23. 23The mileage, XX km per litre of petrol, of a particular model of car is a random variable with mean μ\mu km per litre.…
  24. 24Based on observations over a long period, the mean time taken by male students in Griffles Junior College (GJC) to compl…
  25. 25A factory produces sausage rolls of length 10 cm. The production manager wishes to take a random sample of sausage rolls…
  26. 26EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
  27. 27A firm claims that, on average, their workers spend no more than 8 hours a day at the construction site. The amount of t…
  28. 28A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  29. 29A researcher is running a trial of a new variety of potato. A field contains 20 rows of the new variety of potato plants…
  30. 30The time taken, TT (in minutes), for a 17-year-old student to complete a 5-km run is a random variable with mean 30. Af…
  31. 31Flour is packed in bags of 1.5 kg, as stated on the packaging, by two separate machines A and B in a factory. During a q…
  32. 32Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes – Regular-sized packets an…
  33. 33A batch of plants is grown and then studied to examine how well they are growing. For each plant, data on two indicators…
  34. 34The yield per hectare, yy kg, of a crop is believed to depend on the average rainfall, xx mm, in the month of June. Fo…
  35. 35In a box of cheese rings from a certain manufacturer, the mass of sodium, XX mg, is a continuous random variable with m…
  36. 36Eastham is a football club in a competitive league. It is found that the average time taken by Eastham to score their fi…
  37. 37The waiting time for a patient to see a doctor in a clinic is TT minutes. The waiting times of a randomly chosen sample…
  38. 38Tim is a student in a school with a large student population. As part of his project, Tim would like to interview some o…
  39. 39A chocolate manufacturing company produces chocolate bars. The packaging of the chocolate bar states that the mass of ea…
  40. 40An insurance company declares that the mean payment made on motor insurance claims is $10 000. The auditor examines a r…
  41. 41A random sample of 27 individuals from a population of young men aged 18 was chosen and the length of the right foot of…
  42. 42In a box of cheese rings from a certain manufacturer, the mass of sodium, XX mg, is a continuous random variable with m…
  43. 43In the swimming training school AquaV, the time taken to swim a lap of the pool by the trainees is found to have a mean…
  44. 44Mr Tan, who is the school Admin Manager, believes that JC students in his school take 22 minutes on average to buy and c…
  45. 45A teacher, Mr. Ku, suspects that the average time a student spends on his or her mobile phone per day is μ0\mu_0 minutes…