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Answer :
To test the hypothesis about the population mean body temperature, we begin by setting up the null and alternative hypotheses.
### Step 1: Define the Hypotheses
1. Null Hypothesis (H₀): This is the statement that there is no effect or no difference. It represents the situation where the population mean is equal to a specific value. In this case, we are testing if the population mean body temperature is 98.6°F.
- [tex]\( H_0: \mu = 98.6 \)[/tex]
2. Alternative Hypothesis (H₁): This is the statement that we are testing against the null hypothesis. It represents the situation where the population mean is not equal to the specified value. For this problem, we are testing if the population mean is not 98.6°F.
- [tex]\( H_1: \mu \neq 98.6 \)[/tex]
### Step 2: Choose the Correct Option
Given the hypotheses, we need to identify the correct representation from the provided options. The correct null hypothesis that you would use to test if the population mean is not equal to 98.6 is:
- Option C: [tex]\( H_0: \mu = 98.6 \)[/tex]
This option correctly represents the null hypothesis where the population mean is hypothesized to be 98.6°F.
### Conclusion
The null hypothesis should be stated as [tex]\( H_0: \mu = 98.6 \)[/tex] when we are testing whether the population mean is different from 98.6°F. Therefore, the correct choice for this question is Option C: [tex]\( H_0: \mu = 98.6 \)[/tex].
### Step 1: Define the Hypotheses
1. Null Hypothesis (H₀): This is the statement that there is no effect or no difference. It represents the situation where the population mean is equal to a specific value. In this case, we are testing if the population mean body temperature is 98.6°F.
- [tex]\( H_0: \mu = 98.6 \)[/tex]
2. Alternative Hypothesis (H₁): This is the statement that we are testing against the null hypothesis. It represents the situation where the population mean is not equal to the specified value. For this problem, we are testing if the population mean is not 98.6°F.
- [tex]\( H_1: \mu \neq 98.6 \)[/tex]
### Step 2: Choose the Correct Option
Given the hypotheses, we need to identify the correct representation from the provided options. The correct null hypothesis that you would use to test if the population mean is not equal to 98.6 is:
- Option C: [tex]\( H_0: \mu = 98.6 \)[/tex]
This option correctly represents the null hypothesis where the population mean is hypothesized to be 98.6°F.
### Conclusion
The null hypothesis should be stated as [tex]\( H_0: \mu = 98.6 \)[/tex] when we are testing whether the population mean is different from 98.6°F. Therefore, the correct choice for this question is Option C: [tex]\( H_0: \mu = 98.6 \)[/tex].
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