Math topic中文

Formulation and testing for population mean

Formulation of hypotheses and testing for a population mean based on:

a sample from a normal population of known variance
a large sample from any population

Practice questions

1A nutritionist claims that the mean number of calories in an energy bar is 350 cal. The nutritionist collected and measu…
2The owner of Eng Choo Farm claims that the eggs produced at his farm has an average cholesterol content of $\mu_0$ mg pe…
3A study $^1$ found that students at the National University of Singapore and the Nanyang Technological University sleep a…
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…
5Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
6Researchers at University S claimed that Fungus A, a strain of fungi that is typically found in soil and plants, was a…
7The waiting time for a patient to see a doctor in a clinic is $T$ minutes. The waiting times of a randomly chosen sample…
8Energy bars are a convenient source of nutrition for athletes. A typical energy bar weighs between 30-50 g and is likely…
9Section B: Probability and Statistics [35 marks] From past data, it is known that the mean time taken by students at…
10Korean dramas, or Kdramas, have been immensely popular among students, captivating their attention during leisure hours.…
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…
12During training, the time in seconds for a soldier to dismantle a certain type of equipment is a normally distributed co…
13A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
14A manufacturer claims that the mean lifetime of the light bulbs he produces is at least 1200 hours. A random sample of 1…
15Under normal continuous use, the average battery life of a PI-99 calculator is claimed to be $k$ hours. A random sample…
16In a laboratory, the time in minutes for an inspector to test an electrical circuit board is a continuous random variabl…
17The production manager of a badminton racket company wishes to check that the mean mass of the badminton rackets produce…
18A company produces reinforcing bars for use in construction. The production manager claims that the mean tensile strengt…
19EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
20Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes -- Regular-sized packets a…
21The amount customers spend is often correlated with the amount of time they spend in stores. According to a national sur…
22A hand sanitiser company, Cleanser, claims that the mean volume of each bottle of their hand sanitiser is 15 ml. The con…
23The mileage, $X$ km per litre of petrol, of a particular model of car is a random variable with mean $\mu$ km per litre.…
24Based on observations over a long period, the mean time taken by male students in Griffles Junior College (GJC) to compl…
25A factory produces sausage rolls of length 10 cm. The production manager wishes to take a random sample of sausage rolls…
26EastHam is a football club in a competitive league. It is found that the average time taken by EastHam to score their fi…
27A firm claims that, on average, their workers spend no more than 8 hours a day at the construction site. The amount of t…
28A hospital introduces a new medication regimen to help patients recover from a viral infection more quickly. Previously,…
29A researcher is running a trial of a new variety of potato. A field contains 20 rows of the new variety of potato plants…
30The time taken, $T$ (in minutes), for a 17-year-old student to complete a 5-km run is a random variable with mean 30. Af…
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…
32Mr Dough's factory produces packets of flour for sale in local supermarkets packed in 2 sizes – Regular-sized packets an…
33In a box of cheese rings from a certain manufacturer, the mass of sodium, $X$ mg, is a continuous random variable with m…
34Eastham is a football club in a competitive league. It is found that the average time taken by Eastham to score their fi…
35In an online shop, the time taken, in hours, to sell a watch is a normally distributed continuous random variable $X$ . T…
36The waiting time for a patient to see a doctor in a clinic is $T$ minutes. The waiting times of a randomly chosen sample…
37Tim is a student in a school with a large student population. As part of his project, Tim would like to interview some o…
38Over a period of one month, the increase in heights of orchid plants in a nursery has mean 1.34 cm and standard deviatio…
39A chocolate manufacturing company produces chocolate bars. The packaging of the chocolate bar states that the mass of ea…
40An insurance company declares that the mean payment made on motor insurance claims is $10 000. The auditor examines a r…
41A particular streaming service platform claims that the average time a user spends watching content on the platform per…
42A random sample of 27 individuals from a population of young men aged 18 was chosen and the length of the right foot of…
43In a box of cheese rings from a certain manufacturer, the mass of sodium, $X$ mg, is a continuous random variable with m…
44In the swimming training school AquaV, the time taken to swim a lap of the pool by the trainees is found to have a mean…
45Mr Tan, who is the school Admin Manager, believes that JC students in his school take 22 minutes on average to buy and c…
46A teacher, Mr. Ku, suspects that the average time a student spends on his or her mobile phone per day is $\mu_0$ minutes…