Final Answer:
The appropriate null hypothesis to test the claim that the mean of the population is 100 is option (c): μ = 100.The correct option is c.μ = 100.
Step-by-step explanation:
In hypothesis testing, the null hypothesis (H0) represents the default assumption or status quo, and it is what we aim to test against. In this case, the claim is about the population mean (μ) being 100. The null hypothesis should be formulated in a way that represents no difference or no effect, which aligns with the claim.
Option (c): μ = 100 is the correct null hypothesis because it asserts that the population mean is exactly 100. This is in line with the claim and serves as the baseline for the hypothesis test. Options (a) and (b) would be appropriate in different scenarios, such as when testing if the population mean is greater than or equal to 100 (a: μ ≥ 100) or less than or equal to 100 (b: μ ≤ 100), but they do not directly match the claim made.
To elaborate, if we were to choose option (a), we would be testing whether the population mean is greater than or equal to 100, which might not align with the specific claim that the mean is exactly 100. Similarly, if we were to choose option (b), we would be testing whether the population mean is less than or equal to 100. Therefore, option (c) is the most appropriate null hypothesis for testing the specific claim that the mean of the population is 100.
In summary, the null hypothesis (H0) for this scenario is μ = 100, as it accurately represents the claim being tested and provides a clear baseline for the hypothesis test.
The correct option is c.μ = 100.