Question

For each conjecture, state the null and alternative hypothesis.

a) Null: The average age of community college students is 24.6 years.
Alternative: ____
b) Null: The average score of high school basketball games is less than 88.
Alternative: ____
c) Null: The average age of an attorney is greater than 25.4 years.
Alternative: ____

Answer 1

The alternative hypotheses for the conjectures given are: a) not 24.6 years, b) ≥ 88, and c) ≤ 25.4 years. These hypotheses present the assertions that the research aims to support, differing from the respective null hypotheses.

Step-by-step explanation:

In hypothesis testing, we start with a null hypothesis (H0) which represents the status quo or a specific value to be tested, and an alternative hypothesis (Ha) that states the expected claim or what we are trying to gather evidence for.

For each conjecture given:

1. Null hypothesis: The average age of community college students is 24.6 years.
   Alternative hypothesis: The average age of community college students is not 24.6 years. (Ha: μ ≠ 24.6)
2. Null hypothesis: The average score of high school basketball games is less than 88.
   Alternative hypothesis: The average score of high school basketball games is greater than or equal to 88. (Ha: μ ≥ 88)
3. Null hypothesis: The average age of an attorney is greater than 25.4 years.
   Alternative hypothesis: The average age of an attorney is less than or equal to 25.4 years. (Ha: μ ≤ 25.4)

The alternative hypothesis is what the research is aiming to support; it is a statement that the parameter (like the mean or proportion) has a value that differs from the null hypothesis.