STAT Scientific and Mathematical Reasoning 3

Question 1

A data set of exam scores has a mean of 70 and a standard deviation of 10. If a student scores 90, how many standard deviations above the mean is this score?

Accepted Answer

2

Answer

z = (90 − 70) ÷ 10 = 2, so the score is exactly 2 standard deviations above the mean.

Question 2

When a solid is heated at constant pressure, which energy change primarily occurs at its melting point?

Accepted Answer

Potential energy of particles increases while temperature stays constant

Answer

At the melting point, energy input overcomes intermolecular forces (increases potential energy) without raising temperature.

Question 3

A rectangle has a length that is three times its width. If the area is 75 cm², what is the width?

Accepted Answer

5 cm

Answer

Let width = w; then 3w × w = 75, so 3w² = 75, w² = 25, w = 5 cm.

Question 4

A scientist observes that taller plants produce more seeds. She concludes that height causes increased seed production. What is the main flaw in this reasoning?

Accepted Answer

Correlation does not imply causation — a third factor may explain both

Answer

An observed correlation between two variables cannot establish causality without ruling out confounding factors.

Question 5

Light travels from water (refractive index 1.33) into air (refractive index 1.00). Compared to its speed in water, the speed of light in air is:

Accepted Answer

Faster

Answer

Refractive index = c/v; a lower refractive index means higher speed, so light travels faster in air than in water.

STAT - Special Tertiary Admissions Test Practice Test

STAT - Special Tertiary Admissions Test Practice Test

STAT Scientific and Mathematical Reasoning 3