Question

the statement represents a claim. write its complement and state which is ( h_{0} ) and which is ( h_{a} ).
( sigma<9.1 )
a. ( h_{0}: sigma<9.1 ) (claim); ( h_{a}: sigma geq 9.1 )
b. ( h_{0}: sigma=9.1 ; h_{a}: sigma
eq 9.1 ) (claim)
c. ( h_{0}: sigma leq 9.1 ) (claim); ( h_{a}: sigma>9.1 )
d. ( h_{0}: sigma geq 9.1 ; h_{a}: sigma<9.1 ) (claim)

Explanation:

Step1: Recall the definition of null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality or no difference. The alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. The complement of a statement \(p\) is a statement that is true when \(p\) is false.

Step2: Find the complement of \(\sigma < 9.1\)

The complement of \(\sigma < 9.1\) is \(\sigma\geq9.1\). In hypothesis - testing, the null hypothesis \(H_0\) contains a statement of equality (\(=\), \(\leq\), or \(\geq\)), and the alternative hypothesis \(H_a\) contains a statement of strict inequality (\(<\), \(>\), or \(
eq\)). Since the claim is \(\sigma < 9.1\), the alternative hypothesis \(H_a:\sigma < 9.1\) (claim) and the null hypothesis \(H_0:\sigma\geq9.1\)

Answer:

D. \(H_0:\sigma\geq9.1\); \(H_a:\sigma < 9.1\) (claim)