Question

Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains $10$identical hummingbird feeders and fills $5$, chosen at random, with store-bought food from concentrate and the other $5$with a mixture of sugar and water. The feeders are then randomly assigned to$10$possible hanging locations in the researcher’s yard. Which inference procedure should you use to test whether hummingbirds show a preference for store-bought food based on amount consumed?

(a) A one-sample z test for a proportion .

(b) A two-sample z test for a proportion .

(c) A chi-square test for association/independence .

(d) A two-sample t test .

(e) A paired t test .

Short answer

(d) A two-sample t test .

Step-by-step solution

Given information.

We have been given that,

Number of identical hummingbirds feeders = $10$

Number of feeders filled with store bought food = $5$

Number of feeders filled with sugar mixture = $5$

We need find the procedure for store bought food based on amount consumed.

Simplify.

Feeder $1$: Sugar/Water, for consumed amount.

Feeder $2$: Store bought , for consumed amount.

There are definitely two populations. You will not use the Z test for proportion as that assumes a large sample size of which $10$feeders are not.

The chi square test for independence would not be useful because we only have $1$factor ( sugar water or store bought).

A paired T test is not useful since the observations are not paired in any way.

Therefore, the best answer is (d) a two - sample t test, but because this is a small sample ,it is vitally important the population is normally distributed which may or may not be the case.