Chapter 17Uses and Abuses of Statistics 17.1
Chapter 17Uses and Abuses of Statistics
Warm-up Exercise1.(a)If a machine operates 6 hours a day and produces 30 pieces of products each hour, how many pieces of products are produced in 2 days?
(b)If a machine operates 8 hours a day and produces a piece of product every 2 hours, how many pieces of products are produced in 5 days?
2.Find the mean of each of the following sets of data.
(a)58, 39, 72, 68, 82, 80, 50, 93
(b)$123.8, $95, $100, $78.2, $67.3, $105, $132, $158
3.(a)There are 700 boys and 500 girls in a school. If 120 students are selected with the proportion of boys and girls remainsunchanged, how many boys are selected?
(b)There are 120 red beans and 480 green beans in a bowl. If 100 beans are selected with the proportion of red beans and green beans remainsunchanged, how many green beans are selected?
4.(a)A dice was tossed 100 times and the results were recorded as follows.
Result / Frequency1 / 13
2 / 17
3 / 16
4 / 18
5 / 21
6 / 15
What percentage of the results obtained was smaller than 5?
(b)The table below records the distribution of the time taken by a group of people to finish a certain task.
Time taken (second) / Frequency0-9 / 4
10-19 / 17
20-29 / 35
30-39 / 23
40-49 / 12
50-59 / 9
What percentage of the people takes less than 20 seconds to finish the task?
Build-up Exercise[This part provides three extra sets of questions for each exercise in the textbook, namely Elementary Set, Intermediate Set and Advanced Set. You may choose to complete any ONE set according to your need.]
Exercise 17A
Elementary Set
Level 1
1.Determine whether each of the following cases is a census or a sample survey.
(a)To find the total number of guests in a wedding party, allguests were asked to sign their names at the wedding reception as they arrived.
(b)To investigate the most favourite type of snacks with all the local teenagers between 13 and 18 years old this year, 1000 students between 13 and 18 years old are interviewed.
(c)A teacher collected all test papers of a class of primary two students to check whether they had made corrections to the wrong answers or not.
(d)To determine whether the quality of each carton of lemon tea produced is acceptable or not, one in every 100 cartons of lemon tea is tested.
2.For each of the following cases, determine whether it is a census or a sample survey with brief explanation. If it is a sample survey, describe the population and the sample.
(a)To ensure the braking system of every car works, a car rental company checks the brake of each car before renting it to customers.
(b)To investigate the opinions of foreigners towards the future of Hong Kong, 500 foreigners in the airport were interviewed.
(c)To find the total number of people entering a building one day, a person was sent to record the total number of people entering that building from 8a.m. to 9a.m. on that day.
(d)To investigate the comments of the students on the new design of the school uniform, 20% of the students in a school are asked to fill in a questionnaire.
3.A survey is to be conducted to investigate the ages of people entering the post offices in Hong Kong on a particular day.
(a)Identify the population.
(b)If all people entering the post offices from 2 p.m. to 3 p.m. on that day are interviewed, what is the sample?
(c)If all people entering one of the post offices on that day are interviewed, what is the sample?
4.What type of sampling is used in each of the following cases? Is it a probability sampling or non-probability sampling?
(a)To investigate the comments of the prisoners on the facilities of a prison, 100 randomly selected prisoners are interviewed.
(b)To investigate the attitudes of the students in Chan Ka Wai Secondary School (CKWSS) towards the policy on education, the first 100 CKWSS students arriving at a nearby bus station are interviewed.
(c)A number from 1 to 100 inclusive is generated at random by the computer, say k. Then the kth cup of yogurt in every 100 cups of yogurt is selected for a quality check.
(d)Two members randomly selected from each debate team participating in a debating competition are asked to fill in a questionnaire about the amount of time spent on preparation.
5.Determine whether each of the following is a probability sampling or non-probability sampling. Explain briefly.
(a)Each student in a school has a unique student number. The student union of the school would like to find out the most favourite subject with students by interviewing the students with student numbers divisible by 6.
(b)A hotel manager would like to conduct a survey about the service provided by the hotel. A random number x is selected between 15 and 30, and the manager is going to interview a customer every x minutes tomorrow.
(c)There are 12 girls and 18 boys in a playground. To investigate their most favourite facility in the playground, all the girls and 3 boys randomly selected from the 18 boys are interviewed.
6.Suggest an example of survey targeting at students, which is conducted by using each of the following data collection methods.
(a)Observation
(b)Questioning
7.Suggest an appropriate way to collect data for each of the following surveys.
(a)A survey to investigate the number of lamp posts along a street.
(b)A survey to investigate who is the most favourite teacher with the S5A students.
(c)A survey to investigate the comments of the visitors in a book exhibition.
8.Identify the limitations of the following questions and suggest ways to improve them.
(a)Do you like Saturday and Sunday?
(b)How much did you spend on transportation last year?
(c)What is your religion?
ChristianityBuddhismIslam
(d)Most of the students in this class are going to re-check the marks of English Language in the HKCEE. Are you going to re-check the marks?
(e)Are you satisfied with the arrangement in the Q&A session?
Level 2
9.A worker is going to spend one hour to do the quality check for 1000 zippers. If the worker can check 2 zippers per minute and the sample size for the quality check is expected to be as large as possible, what sample size should be taken?
10.The following shows the number of christmas cards received by 12 primary six students this year.
30, 21, 17, 8, 13, 15, 27, 5, 11, 24, 9, 18
(a)Calculate the mean of the number of christmas cards received by these students.
(b)Choose four students at random and use the number of christmas cards received by them to form a sample. Calculate the mean of the sample and find the sampling error.
(c)Choose eight students at random and use the number of christmas cards received by them to form a sample. Calculate the mean of the sample and find the sampling error.
(Correct your answers to 1 decimal place if necessary.)
11.A teacher would like to find out the average time spent by the secondary five students in the self-study roomeach day. Describe how the teacher could use stratified random sampling to select a sample.
12.A market researcher would like to interview the customers of a restaurant on a particular day. Describe how the researcher could use systematic random sampling to select a sample.
Intermediate Set
Level 1
13.For each of the following cases, determine whether it is a census or a sample survey with brief explanation. If it is a sample survey, describe the population and the sample.
(a)To determine the monthly income of the graduates of an university this year, every graduate coming to the graduation ceremony of this university this year is asked to fill in a questionnaire.
(b)In order to understand the health status of the students in a kindergarten, the principal of the kindergarten collected the medical records of all the students.
(c)To investigate the total number of customers coming to a particular supermarket this month, the total number of customers coming to that supermarket today are counted.
(d)A questionnaire was included in a magazine issued last week to collect the opinions of its readers on a voluntary basis.
14.What type of sampling is used in each of the following cases? Is it a probability sampling or non-probability sampling?
(a)To investigate the opinions of the students about the school singing contest, 30 students walking along a corridor in the school are interviewed.
(b)20 questionnaires are randomly put into the letterboxes of 100 households in a residential building to investigate the attitude of the security guards.
(c)There are 660 boxes of ball pens in red, blue and black.10 boxes of red ball pens, 20 boxes of blue ball pens and 10 boxes of black ball pens are selected at random from these boxes for a quality test.
(d)All the 50 children in a child daycare centre are numbered from 1 to 50 inclusive. A number is then picked at random from 1 to 5 inclusive.All children at intervals of 4 are selected to form a sample starting from whom with the number picked.
15.Suggest an example of survey involving tourism, which is conducted by using each of the following data collection methods.
(a)Observation
(b)Questioning
16.Suggest an appropriate way to collect data for each of the following surveys.
(a)A survey to investigate the occupations of a group of secondary five graduates.
(b)A survey to find out the total number of clinics in Chai Wan.
(c)A survey to determine whether the students are satisfied with the variety offood sold in a school canteen.
17.A survey is to be conducted to study the relation between the exercise patterns and the health status of local people. 20 local people are selected at random from each age group for an interview, and their exercise patterns and health status are recorded.
(a)Identify the sampling method.
(b)Identify the data collection method.
18.Identify the limitations of the following questions and suggest ways to improve them.
(a)How many calls have you received this week?
(b)Are you going to school by bus and MTR?
(c)What will you do if the academic results of your children are unsatisfactory?
Stop all their entertainment
Scold them or beat them
Stop giving them pocket money
(d)Only those who are cold-blooded will not join the voluntary work this weekend. Are you going to join the voluntary work this weekend?
(e)Do you think that the GDP of Hong Kong will increase next year?
Level 2
19.Mrs. Smith would like to spend one hour with her secondary one students to get a general impressionof their spoken English level. She considers using one of the following methods.
Method 1:Select some secondary one students at random, then ask each of them to use 1 minute to comment on the topic provided.
Method 2:Select some secondary one students at random, then divide them into groups of four and ask each group to hold a three-minute discussion on the topic provided.
If she would like to use the method with a larger possible sample size, which method should be used and what sample size should be taken?
20.The following shows the number of passengers on a bus right after it departs from each station.
Station / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9Number of passengers / 5 / 20 / 28 / 40 / 47 / 49 / 52 / 51 / 50
Station / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18
Number of passengers / 36 / 28 / 24 / 22 / 19 / 11 / 9 / 3 / 0
(a)Calculate the mean of the number of passengers on the bus.
(b)Choose five stations at random and use the number of passengers on the bus right after it departs from each of these stations to form a sample. Calculate the mean of the sample and find the sampling error.
(c)Choose ten stations at random and use the number of passengers on the bus right after it departs from each of these stations to form a sample. Calculate the mean of the sample and find the sampling error.
(Correct your answers to 1 decimal place if necessary.)
21.There are 10260 books in a school library. In order to investigate the number of pages of the books in the library, a student would like to conduct a sample survey by inspecting 180 books at random in the library. Based on each of the following sampling methods, briefly describe the selection process for the books to be inspected.
(a)Simple random sampling
(b)Stratified random sampling
(c)Systematic random sampling
(d)Convenience sampling
22.A survey is to be conducted to investigate the amount of time spent on sports each week among 400boys and 600girls in a secondary school.
(a)If 100 students are selected at random for an interview, what type of sampling is used?
(b)If a total of 100 students are selected at random for an interview according to the proportion of the number of boys and girls,
(i)what type of sampling is used?
(ii)how many boys and girls are selected respectively?
(c)It is known that there is a difference between the amount of time spent by boys and girls on sports each week. Which sample, the one selected by using the sampling method in(a) or (b), is more representative?
23.On an aeroplane, there are 324 passengers in the economy class and 36 passengers in the business class. To investigate the comments of the passengers about the flight facilities, 60 passengers will be selected to form a sample.
(a)Write down the name of each of the following sampling methods. Use one of them to select a sample and explain briefly your choice.
(i)Randomly select 60 passengers from those in the economy class.
(ii)Classify all the passengers into different age groups. Then select some passengers at random from each age group to form a sample of 60 passengers.
(iii)Number all the passengers from 1 to 360 inclusive. Then use a computer to generateat random a number from 1 to 6 inclusive. Starting from the number generated, all passengers at intervals of 5 are selected.
(b)It is known that the comments of the passengers in the economy class and the business class may be different. Suggest a reasonable sampling method to select the sample.
Advanced Set
Level 1
24.What type of sampling is used in each of the following cases? Is it a probability sampling or non-probability sampling?
(a)A retailer ordered 10 boxes of potato chips and selected 3 packs of potato chips at random from the top layer in each box to check their expiry dates.
(b)5% of the male workers and 6% of the female workers are selected at random and asked to fill in a questionnaire about the fringe benefits offered by their companies.
(c)In order to plan appropriate services for teenagers,10% of the members of a youth centre are selected at random for an interview.
(d)One day is picked at random from Monday to Sunday. Then that day in each weekof this year is selected to form a sample.
25.Suggest an example of survey involving health care, which is conducted by using each of the following data collection methods.
(a)Observation
(b)Questioning
26.Suggest an appropriate way to collect data for each of the following surveys.
(a)A survey to find out the number of family members among the S5B students.
(b)A survey to investigate the costs of a particular model of digital camera in different shops.
(c)A survey to investigate the average amount of money spent by the tourists from mainland China inHong Kong each month.
27.A furniture shop would like to investigate the preference of the customers for sofa in different materials. Thecustomer records of the shop are listed in order and a random number from 1 to 20 inclusive is selected. Starting from the customer corresponding to the number selected, all customers in the records at intervals of 19 are asked to give some comments on sofa in different materials.
(a)Describe the population and the sample.
(b)Identify the sampling method.
(c)Identify the data collection method.
28.Identify the limitations of the following questions and suggest ways to improve them.
(a)How much time did you spend on sleeping last month?
(b)Do you think that Mathematics is interesting and History is boring?
(c)Do you read newspapers?
Yes, everydayNo, never
(d)The suspect has committed crimes before. Do you believe that he is innocent in this case?
(e)Do you think that CEPA can help improve the economy of Hong Kong?
Level 2
29.A group of four students are doing a project on environmental protection and they would like to spend at most 3 hours to investigate the opinions of people in two districts A and B. Two of them will form a group and each group will be responsible for interviewing people in one district. They would like to interview as many people as they can but the sample size in the two districts must be the same. Suppose each of them can interview 10 people each hour in district A and 8 people each hour in district B, what is the overall sample size in the two districts?
30.The following shows the amount of money spent by Joey in 21 consecutive days.
Day / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11Amount ($) / 45.6 / 55.6 / 68.5 / 64.6 / 50.8 / 104 / 127.6 / 46.6 / 68.6 / 56.4 / 80
Day / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20 / 21
Amount ($) / 45.6 / 107.6 / 56.1 / 57.6 / 65.6 / 34.6 / 71.6 / 58.5 / 103.6 / 114
(a)Calculate the mean amount of money spent by Joey in these 21 days.
(b)Choose 7 days at random and use the amounts spent by Joey in these days to form a sample. Calculate the mean of the sample and find the sampling error.
(c)Choose 14 days at random and use the amounts spent by Joey in these days to form a sample. Calculate the mean of the sample and find the sampling error.
(Correct your answers to 2 decimal places if necessary.)
31.There are 24 storeys in a building with 8 flats on each floor. In order to investigate the comments of the residents on the security of this building, 24 households in this building will be selected at random to fill in a questionnaire. Based on each of the following sampling methods, briefly describe the selection process of the households.
(a)Simple random sampling
(b)Stratified random sampling
(c)Systematic random sampling
(d)Convenience sampling
32.How can the population be divided into groups if stratified random sampling is used in each of the following cases?
(a)A youth centre would like to conduct a survey on the amount of pocket money received by teenagers each week.
(b)An airline company would like to collect the opinions of the customers about the serviceson the flight.
33.Following a concert, 560,462 and 378 questionnaires are collected from the audience at the stalls, upper stalls and balcony respectivelyto investigate the audio effect within the concert hall. To save time of analysis, 200 questionnaires are to be selected to form a sample.
(a)Write down the name of each of the following sampling methods. Use one of them to select a sample and explain briefly your choice.
(i)Randomly select 200 questionnaires from all the questionnaires.
(ii)Take the first 75, 65 and 60 questionnaires from the piles of questionnaires collected from the audience at the stalls, upper stalls and balcony respectively.