State whether each of the following statistical inquiries involves a population or a sample:
To find the relationship between the distance students travel to a specific school and their attendance rate a statistical inquiry is carried out over all the students in the school.
To find the relationship between the maximum height and total horizontal distance of projectiles, 1000 projectiles are launched in an experiment.
To find the relationship between the length and weight of a species of fish, 100 fish are caught and released from a lake.
To find the relationship between the total population of a country and its land area, data for all of the countries in the world is collected.
To find the relationship between the time that the students from a specific school spend studying each night and their phone usage, a statistical inquiry is carried out over all the students in the school.
Describe what the following terms mean with regards to statistical analysis:
Sample
Population
For each of the following populations, give an example of a group of people that make up a sample of the population:
The population is all the students that attend the local high school.
The population is all people aged under 18, who live in Sydney.
The population is all people in a city who play in any organised sporting competition.
The population is all people who own a pet dog.
For each of the following samples, give an example of a population that the sample could have been chosen from:
A sample containing 50 people who drive white cars.
A sample of 50 people drawn from a population. In this sample, the youngest is 18 years old, and the oldest is 64.
A sample containing the first 50 people to enter a train station on a given day.
At a certain chocolate factory, 30\% of products contain nuts. 400 chocolates are tested to check if they meet the required quality for sale. Of those tested, 61\% contained nuts.
What is the population?
State the value of the population proportion.
State the value of the sample proportion.
Do the 400 chocolates tested represent a simple random sample?
State whether or not each of the following samples is biased, giving reasons for your answer:
To investigate the relationship between hours of sleep per night and attention span, 20 test subjects are randomly chosen.
To investigate the relationship between the weight and galloping speed of horses, 20 racehorses are randomly selected from a racing festival.
To investigate the relationship between hours a week spent in cardiovascular training and resting heart rate, 50 men aged between 20 and 30 were randomly sampled.
To investigate the relationship between number of employees and average employee salary in companies worth more than \$10\,000\,000, the 20 richest companies are sampled.
To investigate the relationship between land area and price of houses in a particular suburb, the land area and price of all of the houses in a single street in that suburb were recorded.
To investigate the relationship between the mass of a radioactive material and the amount of nuclear energy released per second, 10 measurements are taken in increments of 1 kg.
To investigate the relationship between the birth weight and life span of elephants, 100 newborn elephants are randomly selected from different regions.
To investigate the relationship between muscle mass and bone density, 30 elderly men were randomly selected.
To investigate the relationship between employee satisfaction and employee salary, the 20 highest paid employees in a company are sampled.
Explain why the following samples are biased:
Hannah is surveying customers at a shopping precinct. She wants to know which stores customers shop at the most. She walks around an entertainment store and chooses 30 customers from the store for the survey.
A TV station wants to know what the most popular type of music is, so they ask listeners to contact them and vote for their favourite type of music.
The community health nurse wants to survey the students in a school about their eating habits. At lunchtime, she stands by a vending machine and surveys every student who purchases something from the machine.
A study is to be conducted to research how sugar affects brain activity. Determine whether the following could result in biased conclusions:
Conducting the study in a country known for high rates of refined food intake.
Having the study funded by a major soft drink manufacturer as they would be able to donate significant funds to the research.
Having the study conducted by a government health agency funded only by the federal government.
Conducting a double blind study where half the participants are in a control group, and the other half are given a treatment. The researchers and participants don't know who is in which group until after the experiment.
After the government decided to increase the minimum retirement age, a news poll selected a group of people to ask their opinions on the changes.
Determine whether the following groups of people should be represented to avoid sampling bias:
People in the community who have a wide variety of views, even if they are not directly affected by the changes.
Only people who are employed.
People in the community who have a wide variety of views, excluding politicians and policy makers.
Only people in the community who would be directly affected by the changes.
The report below is intended to answer whether there is a correlation between age and body mass index (BMI). Discuss any possible ethical issues.
| Name | Age | BMI |
|---|---|---|
| \text{Sarah Williams} | 53 | 28 |
| \text{Ben Patel} | 30 | 23 |
| \text{Peter Singh} | 56 | 25 |
| \text{Luke Li} | 48 | 37 |
| \text{Glen Nguyen} | 52 | 32 |
| \text{Jack Chan} | 45 | 24 |
| \text{Michael Wang} | 24 | 22 |
| \text{Laura Smith} | 47 | 39 |
| \text{Uther Young} | 50 | 21 |
| \text{Beth Brown} | 60 | 35 |
The line of best fit has equation y = 0.27 x + 16.05.
Therefore, there is a positive linear relationship between age and BMI.
The report below is intended to predict the amount of carbon dioxide emitted by a car after using 50 \text{ L} of fuel. Discuss any possible ethical issues.
| \text{Fuel consumption} \\ \text{(L)} | \text{Carbon emission} \\ \text{(kg)} |
|---|---|
| 22 | 59 |
| 40 | 210 |
| 31 | 91 |
| 25 | 84 |
| 30 | 97 |
| 20 | 64 |
| 35 | 106 |
| 28 | 134 |
| 33 | 109 |
| 38 | 121 |
The line of best fit has equation y=3.29x-4.86 and correlation coefficient r=0.31.
Therefore, 50 \text{ L} of fuel will emit 159.64 \text{ kg} of carbon dioxide.
A car company wanted to report on the amount of carbon monoxide emitted by a 2010 model of one of its cars. To do this, it did several test runs using the most recent model of the car. The report below shows the results. Discuss any possible ethical issues.
| \text{Fuel consumption} \\ \text{of current model (L)} | \text{Carbon emission} \\ \text{(kg)} |
|---|---|
| 27 | 90 |
| 22 | 119 |
| 37 | 115 |
| 20 | 70 |
| 35 | 98 |
| 39 | 118 |
| 32 | 97 |
| 40 | 192 |
| 31 | 89 |
| 38 | 121 |
The line of best fit has equation y = 2.58 x + 16.22 and correlation coefficient r = 0.23.
Therefore, the 2010 model emits 145.22 \text{ kg} of carbon monoxide for every 50 \text{ L} of fuel used.