Question

test a claim that the mean amount of lead in the air in u.s. cities is less than 0.036 microgram per cubic meter. it was found that the mean amount of lead in the air for the random sample of 54 u.s. cities is 0.039 microgram per cubic meter and the standard deviation is 0.068 microgram per cubic meter. at \\( \alpha = 0.05 \\), 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 "the mean amount of lead in the air in U.S. cities is less than 0.036 microgram per cubic meter".

Step2: Set up the null hypothesis ($H_0$)

The null hypothesis is the statement of no - effect or equality. So, $H_0:\mu\geq0.036$.

Step3: Set up the alternative hypothesis ($H_a$)

The alternative hypothesis is the claim we are testing. So, $H_a:\mu < 0.036$.

Answer:

$H_0:\mu\geq0.036$; $H_a:\mu < 0.036$; The claim is the alternative ($H_a$) hypothesis.