A researcher selects a sample of [tex]n = 25[/tex] individuals from a population with a mean of [tex]\mu = 103[/tex] 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. [tex]\mu > 103[/tex]

B. [tex]\mu \leq 103[/tex]

C. [tex]\mu \geq 103[/tex]

D. [tex]\mu < 103[/tex]

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 : [tex]H_a: \mu <103[/tex]

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

i.e. Null hypothesis will be : [tex]H_0: \mu \geq103[/tex] (Opposite of alternative hypothesis)

Hence, the correct answer = c. μ ≥ 103