MATH SOLVE

2 months ago

Q:
# 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¯>3.75B. H0:μ=3.75, HA:μ≠3.75C. H0:μ=4.55, HA:μ<4.55D. H0:μ=4.55, HA:μ≠4.55E. H0:μ<4.55, HA:μ=4.55F. H0:x¯=4.55, HA:x¯<4.55

Accepted Solution

A:

Answer: [tex]H_0:\mu=4.55[/tex][tex]H_a:\mu\neq4.55[/tex]Step-by-step explanation:Let [tex]\mu[/tex] 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. [tex]\mu=4.55[/tex]A researcher believes that hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. [tex]\mu\neq4.55[/tex]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[tex]H_0:\mu=4.55[/tex]Alternative hypothesis[tex]H_a:\mu\neq4.55[/tex]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.