High School

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The statement represents a claim. Write its complement and state which is H0 and which is Ha.

mu = 99

A. H0: mu ≥ 99 (claim); Ha: mu < 99
B. H0: mu ≤ 99; Ha: mu > 99 (claim)
C. H0: mu = 99 (claim); Ha: mu ≠ 99
D. H0: mu ≠ 99; Ha: mu = 99 (claim)

Answer :

In hypothesis testing, we formulate two statements: the null hypothesis (H0) and the alternative hypothesis (Ha). These hypotheses are designed to test a claim about a population parameter, often the mean ([tex]\mu[/tex]).

Given the statement [tex]\mu = 99[/tex], we want to write its complement and determine which hypothesis is the null and which is the alternative.

  1. Option A:

    • [tex]H0: \mu \geq 99[/tex] (claim)
    • [tex]Ha: \mu < 99[/tex]

    This option suggests that the claim is that the mean is at least 99, and the alternative hypothesis is that it is less than 99.

  2. Option B:

    • [tex]H0: \mu \leq 99[/tex]
    • [tex]Ha: \mu > 99[/tex] (claim)

    Here, the claim suggests that the mean is greater than 99, and the null hypothesis states it is 99 or less.

  3. Option C:

    • [tex]H0: \mu = 99[/tex] (claim)
    • [tex]Ha: \mu \neq 99[/tex]

    In this scenario, the claim is that the mean is exactly 99, and the alternative is that it is not 99.

  4. Option D:

    • [tex]H0: \mu \neq 99[/tex]
    • [tex]Ha: \mu = 99[/tex] (claim)

    This suggests that the claim is the mean equals 99, assuming the mean is not 99 is the null hypothesis.

The question specifically asks for the complement of [tex]\mu = 99[/tex], which means testing if the mean is any value other than 99. The alternative is [tex]\mu \neq 99[/tex]. Thus, the correct choice in this case is Option C.

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