For each item, detemine the type of sampling method used for these following events:
Drawing out the winning ticket number in a lottery.
Choosing every 50th person on the class roll to take part in a survey.
Choosing 5\% of the of the students in each year for Years 7-12.
Out of 2160 students in a school, 216 were chosen at random and asked their favourite colour out of red, blue and yellow with 99 choosing red, 63 blue and 54 yellow.
One in every how many students at the school was sampled?
Estimate the total number of students in the whole school who prefer the colour:
Red
Blue
Yellow
A television station wants to estimate the number of viewers it had for a new show. They know that the country's population is 13\,620\,000. When they randomly selected 5000 people and asked them if they had watched the show, they found that 400 of them said 'Yes'.
Estimate the number of people who watched the show in the entire population.
A factory produces 3432 iPhones every day. One in every how many iPhones needs to be tested, if the factory is to test a systematic sample of size:
13 iPhones per day.
88 iPhones per day.
A factory produces 1980 laptops every day. How many laptops are tested daily if the factory tests a systematic sample of 1 out of every:
11 laptops.
90 laptops.
In a group of 2160 students, 960 are male and 1200 are female. A stratified sample of 18 is to be selected from the group based on gender.
How many males should be selected?
How many females should be selected?
In a group of 360 students, 90 are primary students and 270 are secondary students. A stratified sample of 120 is to be selected from the group based on year level.
How many primary students should be selected?
How many secondary students should be selected?
A manager wants to randomly select products on an assembly line to test their quality. She generates a random number between 2 and 15, which tells her how many products to pass before picking up the next one. She then generates another random number and so on.
The first product she picks up is the first one on the assembly line. She then generates the following numbers:
10,\,11,\,7,\,14,\,4
How many products did she test in total?
How many products did she pass before picking up the second product?
How many products did she pass between the third and fourth tests?
How many products were in front of the third one she tested?
Users of a particular streaming service can be in one of four categories - Standard, Family, Premium or Business. The table shows the number of people in each category:
How many customers are there across all the categories?
If a stratified sample of 400 is to be taken, state the proportion of the total number people that will be chosen in the sample.
For the sample to be stratified, give the number of customers that should be chosen from each category:
Standard
Family
Premium
Business
| Category | Number of People |
|---|---|
| \text{Standard} | 3500 |
| \text{Family} | 1500 |
| \text{Premium} | 2000 |
| \text{Business} | 3000 |
Four lucky people from a group of 215 each stand to win an iPad. Every contestant is given a different number between 1 and 215, and the winners are selected by generating a random number uniformly between 0 and 1. To ensure there is an equal chance of each contestant winning, the number is multiplied by 215 and then rounded up.
In this case, the numbers generated were:0.152,\, 0.534,\,0.352,\,0.795
Convert the generated numbers into the numbers of the four winning contestants.
A group of people is divided into four teams - Blue, Red, Green and Yellow. The table shows the number of people in each team:
How many people are there combined in all of the teams?
If a stratified sample of 1 in 30 is to be taken from the group, state the size of the sample.
For the sample to be stratified, find the number of people that should be chosen from each team:
Blue team
Red team
Green team
Yellow team
| Team | Number of people |
|---|---|
| \text{Blue} | 150 |
| \text{Red} | 390 |
| \text{Green} | 270 |
| \text{Yellow} | 300 |
Prior to an election, a news editor wanted to view the opinions of randomly selected people. Some two-digit numbers were randomly generated, as shown in the table, and starting with 37, the editor moved 3 to the right, 1 down (so that the next number chosen would be 57). The numbers chosen were the ages of the people she would survey.
| 37 | 49 | 19 | 72 | 38 | 33 | 80 | 83 | 90 | 23 | 78 | 21 | 29 | 72 | 40 |
| 85 | 79 | 84 | 57 | 46 | 49 | 53 | 55 | 51 | 36 | 66 | 61 | 86 | 66 | 41 |
| 74 | 71 | 40 | 49 | 42 | 17 | 50 | 68 | 27 | 15 | 47 | 70 | 47 | 63 | 32 |
| 37 | 33 | 84 | 34 | 35 | 51 | 50 | 87 | 65 | 47 | 38 | 78 | 80 | 39 | 60 |
| 23 | 82 | 64 | 22 | 21 | 76 | 38 | 67 | 43 | 75 | 39 | 76 | 72 | 48 | 33 |
List all the random numbers the editor chose.
Find the range for the ages of the people who will be surveyed.
In a study of asthma sufferers, a group of people are asked to identify which category they fit into:
A - developed asthma from ages 0 to 10
B - developed asthma in their teens
C - developed asthma in their twenties
D - developed asthma after the age of 30
Researchers then generated random values between 0 and 1 to decide which groups to choose participants from. These random values are shown in the given table:
If the number was less than 0.25, the participants were chosen from Category A. How many were chosen from Category A?
If the numbers were greater than 0.75, the participants were chosen from Category D. How many were chosen from Category D?
| 0.750 | 0.574 | 0.145 | 0.154 | 0.564 |
| 0.752 | 0.580 | 0.573 | 0.427 | 0.197 |
| 0.144 | 0.634 | 0.399 | 0.295 | 0.787 |
| 0.971 | 0.643 | 0.313 | 0.169 | 0.979 |
The following table shows the gender of fifty Year 12 students at a particular school:
| Students 1 - 10 | M, F, M, F, F, M, M, M, F, M |
|---|---|
| Students 11 - 20 | M, F, M, M, F, M, F, M, F, F |
| Students 21 - 30 | F, F, M, M, F, M, M, F, F, F |
| Students 31 - 40 | M, F, M, F, F, F, M, M, M, F |
| Students 41 - 50 | F, M, F, M, M, F, M, F, M, F |
Calculate the proportion of females in the sample.
What proportion of the first 5 students were female?
What proportion of the first 10 students were female?
What proportion of the first 20 students were female?
In a systematic sample, every second student is chosen, in the order that they appear, from the first 20 students. How many males will be chosen in the sample?
In a systematic sample, every third student is chosen, in the order that they appear, from the first 40 students. How many females will be chosen in the sample?
The school has a population of 440 students. If the proportion of males and females in the sample is indicative of the whole school, how many female students are there in the school?
Conservationists previously captured, tagged and released 400 whales in a sanctuary. Some time later, a large number of whales were observed, and 34\% were found to be tagged.
Estimate the population of the whales in the sanctuary. Round your answer to the nearest whole number.
Marine biologists want to determine the number of dolphins left along a stretch of coast. They tag 72 dolphins. After a couple of years, they come back to the same area and check 84 dolphins, 12 of which have tags.
What proportion of the dolphins that were checked had tags?
Find the expected population of dolphins along that coast.
The capture-recapture technique was used to estimate the population of cuttlefish. At the beginning of the year, the number of cuttlefish caught, tagged and released was 210. When 700 cuttlefish were taken at the end of the year, 140 of them were found to be recaptured tagged ones.
What percentage of the cuttlefish captured at the end of the year were tagged?
Hence, or otherwise, find the estimated population of cuttlefish in the river.
A researcher captures a sample of 400 fish in a river, tags them and then releases them. The following day, he captures a sample of 1200 fish, of which 100 have tags.
Estimate the number of fish in the river.
A local council wanted to monitor the number of rabbits in the area. They used the capture-recapture technique to estimate the population of rabbits. 219 rabbits were caught, tagged and released. Later, 42 rabbits were caught at random. 15 of these 42 rabbits had been tagged.
Find the estimated population of rabbits. Round your answer to the nearest whole number.
Local council B conducted a similar study and found they had 15\% fewer rabbits. What was the estimated population of rabbits in local council B? Round your answer to the nearest whole number.
A gamekeeper captures a sample of 600 animals, comprised of 100 deer, 300 lions and 200 zebras, tags them and then releases them. The following day, he captures a sample of 200 deer of which 20 are tagged, 1200 lions of which 75 are tagged, and 400 zebras of which 50 are tagged.
Estimate the number of the following animals in the game reserve:
Deer
Lions
Zebras
A researcher captures a sample of 300 fish in a river, tags them and then releases them.
The following day, he captures a sample of 450 fish, of which 75 have tags attached to them. Estimate the number of fish in the river.
The researcher releases back the first sample. The day after that, he captures a sample of 750 fish, of which 30 have tags attached to them. Estimate the number of fish in the river using the results of this sample.
Find the average of the two estimates.
An oil spill has spread over an area of 1650 \text{ km}^{2}. A team of marine biologists scan an area of 150 \text{ km}^2, and find 272 dead marine animals.
Find an estimate for the number of dead marine animals over the entire area of the oil spill.