Math topic中文

Concepts and terminology

Concepts of null hypothesis H0H_0 and alternative hypotheses H1H_1, test statistic, critical region, critical value, level of significance, and pp-value.

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 study1^1 found that students at the National University of Singapore and the Nanyang Technological University sleep a…
  4. 4A bakery claims that the mass of a cake, on average, is 600 grams each. A random sample of 10 cakes is examined and the…
  5. 5Researchers at University S claimed that Fungus A, a strain of fungi that is typically found in soil and plants, was a…
  6. 6The waiting time for a patient to see a doctor in a clinic is TT minutes. The waiting times of a randomly chosen sample…
  7. 7Energy bars are a convenient source of nutrition for athletes. A typical energy bar weighs between 30-50 g and is likely…
  8. 8Section B: Probability and Statistics [35 marks] From past data, it is known that the mean time taken by students at…
  9. 9Korean dramas, or Kdramas, have been immensely popular among students, captivating their attention during leisure hours.…
  10. 10During training, the time in seconds for a soldier to dismantle a certain type of equipment is a normally distributed co…
  11. 11A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  12. 12A manufacturer claims that the mean lifetime of the light bulbs he produces is at least 1200 hours. A random sample of 1…
  13. 13Under normal continuous use, the average battery life of a PI-99 calculator is claimed to be kk hours. A random sample…
  14. 14In a laboratory, the time in minutes for an inspector to test an electrical circuit board is a continuous random variabl…
  15. 15The production manager of a badminton racket company wishes to check that the mean mass of the badminton rackets produce…
  16. 16A company produces reinforcing bars for use in construction. The production manager claims that the mean tensile strengt…
  17. 17EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
  18. 18Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
  19. 19The amount customers spend is often correlated with the amount of time they spend in stores. According to a national sur…
  20. 20A hand sanitiser company, Cleanser, claims that the mean volume of each bottle of their hand sanitiser is 15 ml. The con…
  21. 21The mileage, XX km per litre of petrol, of a particular model of car is a random variable with mean μ\mu km per litre.…
  22. 22Based on observations over a long period, the mean time taken by male students in Griffles Junior College (GJC) to compl…
  23. 23A factory produces sausage rolls of length 10 cm. The production manager wishes to take a random sample of sausage rolls…
  24. 24EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
  25. 25A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
  26. 26A researcher is running a trial of a new variety of potato. A field contains 20 rows of the new variety of potato plants…
  27. 27The 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…
  28. 28Flour 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…
  29. 29Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes – Regular-sized packets an…
  30. 30In a box of cheese rings from a certain manufacturer, the mass of sodium, XX mg, is a continuous random variable with m…
  31. 31Eastham is a football club in a competitive league. It is found that the average time taken by Eastham to score their fi…
  32. 32In an online shop, the time taken, in hours, to sell a watch is a normally distributed continuous random variable XX. T…
  33. 33Tim is a student in a school with a large student population. As part of his project, Tim would like to interview some o…
  34. 34A chocolate manufacturing company produces chocolate bars. The packaging of the chocolate bar states that the mass of ea…
  35. 35An insurance company declares that the mean payment made on motor insurance claims is $10 000. The auditor examines a r…
  36. 36A particular streaming service platform claims that the average time a user spends watching content on the platform per…
  37. 37A random sample of 27 individuals from a population of young men aged 18 was chosen and the length of the right foot of…
  38. 38In a box of cheese rings from a certain manufacturer, the mass of sodium, XX mg, is a continuous random variable with m…
  39. 39In the swimming training school AquaV, the time taken to swim a lap of the pool by the trainees is found to have a mean…
  40. 40Mr Tan, who is the school Admin Manager, believes that JC students in his school take 22 minutes on average to buy and c…
  41. 41A teacher, Mr. Ku, suspects that the average time a student spends on his or her mobile phone per day is μ0\mu_0 minutes…