Question

A researcher selects a sample of n = 25 individuals from a population with a mean of μ = 103 and administers a treatment to the sample. If the research predicts that the treatment will decrease scores, then what is the correct statement of the null hypothesis for a directional (one-tailed) test?

a. μ > 103
b. μ ≤ 103
c. μ ≥ 103
d. μ < 103

Answer 1

Answer: c. μ ≥ 103

Explanation:

We know that , the null hypothesis and alternative hypothesis basically describes the objective for the test and contains the population parameter but both are against to each other.

Null hypothesis takes '=' , '≤' , '≥' signs .

Alternative hypothesis takes '≠' , '<' , '>' signs.

As per given , we have

A researcher selects a sample of n = 25 individuals from a population with a mean of μ = 103 and administers a treatment to the sample.

If the research predicts that the treatment will decrease scores i..e μ < 103.

i.e. Alternative hypothesis :
`H_a: \mu <103`

Against this the treatment can increase the scores or remains equal.

i.e. Null hypothesis will be :
`H_0: \mu \geq103` (Opposite of alternative hypothesis)

Hence, the correct answer = c. μ ≥ 103