Question

What is the relationship between the temperature (x-axis - independent variable) and bounce height (y-axis - dependent variable)? Is it Positive or Negative or neither and Explain Why you know that?

a) Positive; As temperature increases, bounce height increases.
b) Negative; As temperature increases, bounce height decreases.
c) Neither; There is no clear relationship between temperature and bounce height.


Make a "Claim" about how the temperature of the ball affects the height that it bounces.
a) Claim: Higher temperature results in higher bounce height.
b) Claim: Higher temperature results in lower bounce height.
c) Claim: Temperature has no effect on bounce height.
d) No claim made.

Describe why the evidence you provided supports your claim.
a) It's evident because the data shows a clear pattern.
b) The evidence does not support the claim made.
c) The evidence is inconclusive.
d) No evidence provided.

Answer 1

A positive correlation between temperature and bounce height would suggest that as temperature increases, so does bounce height. Real-world physics suggests this correlation is likely positive since materials often become more elastic with higher temperatures, increasing the bounce height of a ball. However, a claim must be supported by empirical data showing a consistent increase in bounce height with temperature.

Step-by-step explanation:

The relationship between the temperature (independent variable) and bounce height (dependent variable) can be identified as either positive or negative based on whether the bounce height increases or decreases with temperature. If there is a positive correlation, as the temperature increases, the bounce height would also increase. Conversely, a negative correlation would mean that as the temperature increases, the bounce height decreases. Evidence from real-world physics suggests that as temperature increases, the elasticity of the material in a ball typically also increases, causing the ball to bounce higher. Therefore, the most likely claim that can be made is that a higher temperature results in a higher bounce height, indicating a positive correlation.

Several examples support this understanding, such as the relationship between ice cream sales and crime rates, which both increase when temperatures are warmer, indicating a positive correlation. Furthermore, in economics, it is observed that price and quantity demanded have a negative relationship, as higher prices lead to lower demand. However, when making any claim about a correlation, it is necessary to have empirical data that clearly shows a pattern or trend between the two variables under consideration.

For the question at hand, to support the claim that a higher temperature results in a higher bounce height, one would look for data showing a consistent pattern where bounce height increases with an increase in temperature. If such evidence is available and shows a clear pattern, then Claim (a): Higher temperature results in higher bounce height is supported. Absent this data, making any claim would be speculative.