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 the amount consumed?

a. A one-sample $z-$test for a proportion

b. A two-sample $z-$test for a difference in proportions

c. A chi-square test for independence

d. A two-sample t-test

e. A paired t-test

Short answer

The correct option is (d) A two-sample $t-$test

Step-by-step solution

Given information

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.

Explanation

There are ten feeders in total: five with water/sugar and five with store-bought food. To avoid bias, everything is randomised. As a result, the data will look like this:

Feeder 1: Sugar/Water - for the amount consumed

Feeder 2: Store-bought - for the amount consumed

And so forth. There are two distinct populations. For proportion, you will not utilise the $z-$test because it requires a big sample size.

Because we only have one factor, the chi-square test for independence would be useless (sugar water or store-bought).

Because the observations are not paired in any way, a paired $T-$test is useless.

As a result, a two-sample $t-$test is the best option, but because this is a tiny sample, it's critical that the population is normally distributed, which may or may not be the case. As a result, option (d) is the proper choice.