Question

there is a negative correlation between tv watching and grades. what can we conclude from this research finding?
○ we can conclude that this is an illusory correlation.
○ we can conclude that tv watching leads to lower grades.
○ we can conclude that tv watching leads to higher grades.
○ we can conclude that a student who watches a lot of tv is likely to have lower grades.

pregunta 28
1 puntos
which of the following groups of scores would have the smallest standard deviation (remember, look at how the scores vary from the average--it is a measure of variance or spread)?
○ 20,40,60,80,100
○ 2,4,6,8,10
○ 5,15,25,35,45
○ 100,200,300,400,500

Explanation:

First Question (Correlation Interpretation)

• An illusory correlation is a false perception of a relationship, but here a negative correlation is found (not illusory), so first option is wrong.
• Correlation does not imply causation, so we can’t conclude TV watching leads to lower grades (second option wrong) or higher grades (third option wrong, as negative correlation means inverse relationship).
• A negative correlation means as one variable (TV watching) increases, the other (grades) tends to decrease. So a student who watches a lot of TV is likely to have lower grades (fourth option is correct as it describes the trend, not causation).

Step1: Recall standard deviation concept

Standard deviation measures the spread of data. Smaller spread (less variation from the mean) means smaller standard deviation. We analyze the difference between consecutive scores (or the "step" between scores) for each group.

Step2: Analyze each group

• Group 1: \(20, 40, 60, 80, 100\) – difference between consecutive scores is \(20\) (e.g., \(40 - 20 = 20\), \(60 - 40 = 20\), etc.).
• Group 2: \(2, 4, 6, 8, 10\) – difference between consecutive scores is \(2\) (e.g., \(4 - 2 = 2\), \(6 - 4 = 2\), etc.).
• Group 3: \(5, 15, 25, 35, 45\) – difference between consecutive scores is \(10\) (e.g., \(15 - 5 = 10\), \(25 - 15 = 10\), etc.).
• Group 4: \(100, 200, 300, 400, 500\) – difference between consecutive scores is \(100\) (e.g., \(200 - 100 = 100\), \(300 - 200 = 100\), etc.).

Step3: Compare spreads

The group with the smallest step between scores (smallest variation) will have the smallest standard deviation. Group 2 (\(2, 4, 6, 8, 10\)) has the smallest step (\(2\)) between consecutive scores, so its data is least spread out.

Answer:

We can conclude that a student who watches a lot of TV is likely to have lower grades.

Second Question (Standard Deviation)