For the given conjecture, we want to determine the null and alternative hypotheses related to the average age of community college students.
a) The null hypothesis (H0) typically represents the status quo or the claim being tested. In this case, it asserts that the average age of community college students is equal to the conjectured value.
b) The alternative hypothesis (H1 or Ha) represents a statement that contradicts the null hypothesis. It usually reflects what one might conclude if the null hypothesis is rejected.
Therefore, we can formulate the hypotheses as follows:
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The null hypothesis (H0): The average age of community college students is 24.6 years.
Mathematically, this can be expressed as: \[ H_0: \mu = 24.6 \]
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The alternative hypothesis (H1): The average age of community college students is not 24.6 years.
Mathematically, this can be expressed as: \[ H_1: \mu \neq 24.6 \]
In summary:
- The null hypothesis is \( H_0: \mu = 24.6 \)
- The alternative hypothesis is \( H_1: \mu \neq 24.6 \)