For each scenario below, choose the best way to gather data from the following options:
Conduct an observational study
Conduct an experiment
Look up official data
Finding the conductivity of a piece of metal at different temperatures.
Investigating the relationship between the heights of basketball players and the number of points that they score.
Investigating the effect of changing water temperature on shark populations.
Investigating the relationship between the size of fish and the maximum depth they can swim down to.
For each scenario below, choose the most appropriate statistic to use from the following options:
Gradient of line of best fit
y-intercept of line of best fit
Correlation coefficient
Extrapolation from the data
Interpolation from the data
Finding the strength of the relationship between an individual's ability in mathematics and their ability in music.
Finding the rate of change of house prices over a number of years.
Finding the initial population of a bacterial culture in an experiment to see how quickly bacteria reproduce.
Finding the height of a tree in the 5th year if the heights in the 1st, 4th and 7th years were recorded.
Finding the strength of the relationship between an individual's heart rate and their energy intake.
Predicting the average yearly temperature for a year in the future.
In an inquiry to find the energy consumption of a car, 10 controlled experiments were performed and the data were gathered below:
| x | 147 | 259 | 317 | 403 | 448 | 660 | 705 | 751 | 756 | 771 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 25 | 35 | 41 | 49 | 47 | 76 | 72 | 77 | 82 | 82 |
The correlation coefficient was found to be r = 0.99, and the line of best fit was found to be \\ y = 0.09 x + 11.23, where x is the distance in \text{km} and y is the pretrol consumed in \text{L}.
What can we conclude from this inquiry?
In an inquiry to find the relationship between height and hair length, the data from 10 people have been recorded below:
| x | 169.2 | 188 | 153.1 | 164.4 | 161.4 | 169.2 | 197.8 | 191.2 | 177.7 | 161 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 15.1 | 17.42 | 25.38 | 26.11 | 0.37 | 32.01 | 21.56 | 13.11 | 49 | 10.32 |
The correlation coefficient was found to be r = 0.09, and the line of best fit was found to be y = 0.08 x + 6.52, where x is the height (in centimetres) and y is the hair length (in centimetres).
What can we conclude from this inquiry?
In an inquiry to find the healthcare spending per capita of a country which did not release such data, the healthcare spending per capita and life expectancies of 10 countries were recorded below:
| x | 86.5 | 75.7 | 86.2 | 81.3 | 82 | 85.7 | 89.9 | 85.9 | 92.2 | 77.2 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 7278 | 1894 | 7112 | 2691 | 4044 | 5874 | 7481 | 2968 | 7632 | 3606 |
The correlation coefficient was found to be r = 0.83, and the line of best fit was found to be y = 356.3443 x - 24967.57, where x is the life expectacy and y is the health expenditure per capita.
The health expenditure per capita of a country with a life expectancy of 76 was then predicted to be y = 2114.6.
What can we conclude from this inquiry?
In an inquiry to find how effective studying 60 hours a week is on test results, the data below were gathered:
| x | 10 | 27 | 20 | 21 | 26 | 18 | 19 | 26 | 17 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 59 | 80 | 67 | 72 | 79 | 65 | 69 | 78 | 68 | 67 |
The correlation coefficient was found to be r = 0.97, and the line of best fit was found to be y = 1.24 x + 45.56.
For a studying time of 60 hours a week (x = 60) it was predicted that the correlated test score would be y = 120.08.
What can we conclude from this inquiry?
Scientists conducted a study to see people's reaction times after they've had different amounts of sleep. The results are recorded in the table:
| \text{Number of hours of sleep} \left(x\right) | 1.1 | 1.5 | 2.1 | 2.5 | 3.5 | 4 |
|---|---|---|---|---|---|---|
| \text{Reaction time in seconds} \left(y\right) | 4.66 | 4.1 | 4.66 | 3.7 | 3.6 | 3.4 |
The data has been graphed along with a line of best fit:
Calculate the correlation coefficient for this data to two decimal places.
Find the equation of the line of best fit. Round all values to two decimal places.
What can we conclude from this inquiry?
The number of fish in a river is measured over a five year period:
| \text{Time in years}\, (t\text{)} | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| \text{Number of fish } (F\text{)} | 1903 | 1994 | 1995 | 1602 | 1695 | 1311 |
The data has been graphed along with a line of best fit:
Calculate the correlation coefficient for this data to two decimal places.
Find the equation of the line of best fit. Round all values to one decimal place.
Predict the number of years until there are no fish left in the river.
What can we conclude from this inquiry?
The following table shows the temperature of a cooling metal versus the number of minutes that have passed:
| \text{Minutes }(x) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| \text{Temperature }(y) | 29 | 25 | 25 | 21 | 21 | 17 |
Construct a scatter plot for this data on a number plane.
Sketch the line of best fit for the data, given that the line passes through \left(2, 26\right) and \left(6, 18\right).
Calculate the correlation coefficient for this data to two decimal places.
What can we conclude from this inquiry?