Question

For each statement, select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

(a) A certain type of hummingbird is known to have an average weight of 4.55 grams. A researcher believes that hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. The researcher finds a sample of 30 such hummingbirds from the Grand Canyon and calculates their average weight to be 3.75 grams. (Here μ represents the population mean weight of hummingbirds who live in the Grand Canyon.)
A. H0:x¯=3.75, HA:x¯>3.75
B. H0:μ=3.75, HA:μ≠3.75
C. H0:μ=4.55, HA:μ<4.55
D. H0:μ=4.55, HA:μ≠4.55
E. H0:μ<4.55, HA:μ=4.55
F. H0:x¯=4.55, HA:x¯<4.55

Answer 1

Answer:
`H_0:\mu=4.55`

`H_a:\mu\\eq4.55`

Explanation:

Let
`\mu` be the population mean weight of hummingbirds who live in the Grand Canyon.

Given : A certain type of hummingbird is known to have an average weight of 4.55 grams.

i.e.
`\mu=4.55`

A researcher believes that hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole.

`\mu\\eq4.55`

We know that null hypothesis shows there is no statistical difference between the group being tested on the other hand alternative hypothesis believes that there is statistical difference between them.

Then , the appropriate hypothesis for the given situation:

Null hypothesis
`H_0:\mu=4.55`

Alternative hypothesis
`H_a:\mu\\eq4.55`

Note : 3.75 grams is just a sample mean of 30 humming birds (not entire population) , so it has no relation with establishment for the null hypothesis and alternative hypothesis.