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Answer :
To address the problem, let's first understand some key concepts about hypotheses in statistics. In hypothesis testing, you generally have two hypotheses:
Null Hypothesis (H0): This is a statement of no effect, difference, or change. It is usually a statement that the observed data is due to chance.
Alternative Hypothesis (Ha): This is what you aim to prove. It represents a new effect, difference, or change that the study is estimating or testing.
Now, let's examine the given statement: mu = 8.3 which expresses a claim about the population mean (mu).
To complement this statement, we need to consider the context of hypothesis testing:
A. H0: mu = 8.3 (claim); Ha: mu ≠ 8.3
- This option presents the null hypothesis as mu = 8.3, which means under the null hypothesis, the population mean is exactly 8.3. The alternative hypothesis is mu ≠ 8.3, suggesting that the population mean is not equal to 8.3.
B. H0: mu ≥ 8.3 (claim); Ha: mu < 8.3
- Here, the null hypothesis is set as mu ≥ 8.3, and the alternative hypothesis is mu < 8.3.
C. H0: mu ≤ 8.3; Ha: mu > 8.3 (claim)
- In this scenario, the null hypothesis suggests that mu ≤ 8.3, implying the population mean is no more than 8.3, while the alternative hypothesis, stated as the claim, is mu > 8.3.
D. H0: mu ≠ 8.3; Ha: mu = 8.3 (claim)
- This option reverses the standard view, setting the null hypothesis as mu ≠ 8.3 and the alternative as mu = 8.3. This is uncommon as null hypotheses are typically tested as statements of equality.
Correct Answer: A. H0: mu = 8.3 (claim); Ha: mu ≠ 8.3
In standard practice, the null hypothesis (H0) contains the equality, and the alternative hypothesis (Ha) is its complement which, in this case, is that mu is not equal to 8.3. This option best represents a typical statistical test setup when the claim is that the population mean is exactly a certain value.
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