Question

Kendra reads in Modern Dog Magazine that the average age of dogs currently alive is 4.8 years. To determine if this finding applies to the customers in her pet store, Kendra surveys every fifth customer in her store who owns a dog and asks the age of their dog. She collects data for seven weeks and obtains the following averages.

Week Average Age (in years)
1 3.7
2 3.8
3 4.2
4 4.1
5 3.9
6 3.9
7 4.0
Select the statement that is true about Kendra's sample.
a) Kendra's samples are both accurate and precise.
b) Kendra's samples are precise but not accurate.
c) Kendra's samples are neither accurate nor precise.
d) Kendra's samples are accurate but not precise.

Answer 1

Kendra's samples are precise but not accurate.

Explanation:

To be accurate and precise they should be around 4.8 for all the measures. We can see that they are all relatively close to one another (between 3.7 and 4.2), so they are precise. However, they are all are smaller than 4.8, so they are not accurate.

Answer 2

The true statement about Kendra's sample is:

b) Kendra's samples are precise but not accurate.

Explanation:

a) Data and Calculations:

Average age of dogs currently alive = 4.8 years

Average ages of dogs in Kendra's sample

Week Average Age (in years)

1 3.7

2 3.8

3 4.2

4 4.1

5 3.9

6 3.9

7 4.0

Total 27.6

Mean = 3.9 (27.6/7)

b) Accuracy refers to how close Kendra's sample mean age of dogs is to the average age value as stated in the Modern Dog Magazine. While the Magazine stated an average age of 4.8 years, Kendra's sample produced a mean of 3.9 years. On the other hand, precision refers to how close Kendra's sample measurements are to each other. With a mean of 3.9 years, the sample measurements are very close to each other. Therefore, we can conclude that "Kendra's samples are precise but not accurate."