Question

test a claim that the mean amount of lead in the air in u.s. cities is less than 0.037 microgram per cubic meter. it was found that the mean amount of lead in the air for the random sample of 56 u.s. cities is 0.038 microgram per cubic meter and the standard deviation is 0.068 microgram per cubic meter. 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 \\). \\( h_0 \\): \\( h_a \\): (type integers or decimals. do not round.) the claim is the hypothesis.

Explanation:

Step1: Identify the claim

The claim is that the mean amount of lead in the air in U.S. cities is less than \(0.037\) microgram per cubic meter.

Step2: Set up the null and alternative hypotheses

The null hypothesis \(H_{0}\) is the statement of equality. So, \(H_{0}:\mu\geq0.037\).
The alternative hypothesis \(H_{a}\) is the claim. So, \(H_{a}:\mu < 0.037\).

Answer:

\(H_{0}:\mu\geq0.037\), \(H_{a}:\mu < 0.037\). The claim is the alternative (\(H_{a}\)) hypothesis.