Question

test a claim that the mean amount of carbon monoxide in the air in u.s. cities is less than 2.32 parts per million. it was found that the mean amount of carbon monoxide in the air for the random sample of 65 cities is 2.38 parts per million and the standard deviation is 2.11 parts per million. at \\( \alpha = 0.01 \\), can the claim be supported? complete parts (a) through (e) below. assume the population is normally distributed.
(a) identify the claim and state \\( h _ { 0 } \\) and \\( h _ { a } \\). which of the following correctly states \\( h _ { 0 } \\) and \\( h _ { a } \\)?
\\( h _ { 0 } \\):
\\( h _ { a } \\):
(type integers or decimals. do not round.)
the claim is the hypothesis.

Explanation:

Step1: Identify the claim

The claim is "the mean amount of carbon monoxide in the air in U.S. cities is less than 2.32 parts per million".

Step2: State the null and alternative hypotheses

The null hypothesis \(H_0\) is a statement of equality. The alternative hypothesis \(H_a\) is the claim we are testing.
Since the claim is about the mean (\(\mu\)) being less than 2.32, the null hypothesis \(H_0:\mu\geq2.32\) (opposite of the claim for the equality - based on the form of hypothesis testing where \(H_0\) has \(\leq\),\(\geq\), or \(=\) and \(H_a\) has \(>\),\(<\), or \(
eq\)) and the alternative hypothesis \(H_a:\mu < 2.32\).

Answer:

\(H_0:\mu\geq2.32\), \(H_a:\mu < 2.32\). The claim is the alternative (\(H_a\)) hypothesis.