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Use the given statement to represent a claim. Write its complement and state which is $H_{0}$ and which is $H_{x}$ $\newline$ $\mu \leq 509$ $\newline$ Find the complement of the claim. $\newline$ $((\square09)/(\mu))$ $\newline$ Which is $H_{0}$ and which is $H_{2}$ ? $\newline$ A. $H_{0}:\mu \leq 509$ $\newline$ B. $H_{0}:\mu \geq 509$ $\newline$ C. $H_{0}:\mu \leq 509$ $\newline$ $H_{8}:\mu < 509$ $\newline$ $H_{x}$ $0$ $\newline$ D. $\newline$ $H_{x}$ $1$ $\newline$ E. $H_{0}:\mu \leq 509$ $\newline$ $H_{x}$ $3$ $\newline$ F. $\newline$ $H_{x}$ $4$ $\newline$ G. $H_{0}:\mu \leq 509$ $\newline$ H. $H_{x}$ $6$ $\newline$ L. $\newline$ $H_{x}$ $7$

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Solve two-step equations: word problems

Full solution

Q. Use the given statement to represent a claim. Write its complement and state which is

H_{0}

and which is

H_{x}

\newline

\mu \leq 509

\newline

Find the complement of the claim.

\newline

((\square09)/(\mu))

\newline

Which is

H_{0}

and which is

H_{2}

?

\newline

A.

H_{0}:\mu \leq 509

\newline

B.

H_{0}:\mu \geq 509

\newline

C.

H_{0}:\mu \leq 509

\newline

H_{8}:\mu < 509

\newline

H_{x}

0

\newline

D.

\newline

H_{x}

1

\newline

E.

H_{0}:\mu \leq 509

\newline

H_{x}

3

\newline

F.

\newline

H_{x}

4

\newline

G.

H_{0}:\mu \leq 509

\newline

H.

H_{x}

6

\newline

L.

\newline

H_{x}

7

Understand and Identify: Understand the given claim and identify the null hypothesis ( $H_0$ ). The given claim is $\mu \leq 509$ . In hypothesis testing, the null hypothesis ( $H_0$ ) is typically a statement of no effect or no difference, and it is the hypothesis that we assume to be true until we have enough evidence to support an alternative hypothesis. Therefore, the null hypothesis in this case is $H_0: \mu \leq 509$ .
Determine Alternative Hypothesis: Determine the complement of the given claim to identify the alternative hypothesis $H_a$ . The complement of the claim $\mu \leq 509$ is that $\mu$ is greater than $509$ , which can be written as $\mu > 509$ . This is the alternative hypothesis $H_a$ because it is the statement that we are trying to find evidence for against the null hypothesis.
Write Hypotheses: Write the null and alternative hypotheses correctly. $\newline$ Based on the given claim and its complement, we can write the null hypothesis ( $H_0$ ) and the alternative hypothesis ( $H_a$ ) as follows: $\newline$ $H_0: \mu \leq 509$ (the claim) $\newline$ $H_a: \mu > 509$ (the complement of the claim)
Match Correct Option: Match the hypotheses to the correct option. $\newline$ Looking at the options provided, we need to find the one that correctly states the null hypothesis as $H_0: \mu \leq 509$ and the alternative hypothesis as $H_a: \mu > 509$ . The correct option is: $\newline$ F. \left\{\begin{array}{l}H_0: \mu \leq 509\H_a: \mu > 509\end{array}\right.

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