Question

Here are some summary statistics for the life spans of two breeds of cats.

Breed Mean life span Standard deviation
Abyssinian μ=12 years σ=1.5 years
Colorpoint shorthair μ=14 years σ=1 year

Fluffy was an Abyssinian cat who lived for 13 years, and Mittens was a colorpoint shorthair cat who lived for 15 years.

Relative to its breed, which cat had a longer lifespan?

a. It is impossible to say without seeing all of the individual lifespans.
b. Fluffy
c. Fluffy and Mittens had equally long lifesparlsrelative to their breeds.
d. Mittens

Answer 1

D: Mittens

Explanation:

We are given;

Population mean;

- Abyssinian: μ = 12

- Colorpoint shorthair: μ = 14

Population standard deviation;

- Abyssinian: σ = 1.5

- Colorpoint shorthair: σ = 1

Sample mean;

-Fluffy the Abyssinian: x¯ = 13

-Mittens the colorpoint shorthair; x¯ = 15

To find which cat had a longer lifespan, we need to find the z-score for both breeds and the one with the higher z-score is the one with longer lifespan.

Z-score formula is;

z = (x¯ - μ)/σ

For Fluffy the Abyssinian;

z = (13 - 12)/1.5

z = 0.667

For Mittens the colorpoint shorthair;

z = (15 - 14)/1

z = 1

Z-score of Mittens is higher and thus it has a longer lifespan.