Question

the statement represents a claim. write its complement and state which is ( h_{0} ) and which is ( h_{a} ).
( mu = 8.8 )
a. ( h_{0}: mu leq 8.8 ; h_{a}: mu>8.8 ) (claim)
b. ( h_{0}: mu geq 8.8 ) (claim); ( h_{a}: mu<8.8 )
c. ( h_{0}: mu
eq 8.8 ; h_{a}: mu = 8.8 ) (claim)
d. ( h_{0}: mu = 8.8 ) (claim); ( h_{a}: mu
eq 8.8 )

Explanation:

Step1: Recall the definitions of null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_A\) is a statement that contradicts \(H_0\).

Step2: Analyze each option

• Option A: \(H_0:\mu\leq8.8\) is not an equality statement (the claim \(\mu = 8.8\) is not represented correctly here).
• Option B: \(H_0:\mu\geq8.8\) is not an equality statement (the claim \(\mu = 8.8\) is not represented correctly here).
• Option C: \(H_A:\mu = 8.8\) is an equality statement. But by convention, \(H_0\) should be the equality statement.
• Option D: \(H_0:\mu = 8.8\) (the claim) is an equality statement. \(H_A:\mu

eq8.8\) is the complement (opposite) of \(H_0\).

Answer:

D. \(H_0:\mu = 8.8\) (claim); \(H_a:\mu
eq8.8\)