Question

attendance the attendance, in hundreds of people, at an aquarium and a zoo each day is shown.
is there a correlation between the variables in the data? is there likely causation?
a) correlation but no causation
b) positive correlation and causation
c) negative correlation and causation
d) neither correlation nor causation

Explanation:

Step1: Analyze the data

Let's list out the data points. For the aquarium attendance (in hundreds) \(x\): \(5,1,1,8,7,5,9\). For the zoo attendance (in hundreds) \(y\): \(3,5,6,2,3,5,1\).

Step2: Check for correlation

We can see that when \(x = 5\), \(y=3\) or \(5\); when \(x = 1\), \(y = 5\) or \(6\); when \(x=8\), \(y = 2\); when \(x = 7\), \(y=3\); when \(x=9\), \(y = 1\). There is no clear increasing or decreasing trend. For example, as the aquarium attendance (\(x\)) increases from \(1\) (day \(2\)) to \(8\) (day \(4\)), the zoo attendance (\(y\)) decreases from \(5\) to \(2\). But when \(x\) increases from \(5\) (day \(1\)) to \(7\) (day \(5\)), \(y\) decreases from \(3\) to \(3\) (no clear trend) in some cases.

Step3: Check for causation

Causation means that a change in one variable causes a change in another variable. There is no logical reason that the number of people at an aquarium would directly cause a change in the number of people at a zoo. They are two separate attractions.

Answer:

A. correlation but no causation