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 57 u.s. cities is 0.039 microgram per cubic meter and the standard deviation is 0.069 microgram per cubic meter. at \\( \alpha = 0.10 \\), can the claim be supported? complete parts (a) through (e) below. assume the population is normally distributed.

(c) find the standardized test statistic, t.
the standardized test statistic is \\( t = 0.22 \\).
(round to two decimal places as needed.)

(d) decide whether to reject or fail to reject the null hypothesis.
fail to reject \\( h _ { 0 } \\) because the standardized test statistic is not in the rejection region.

(e) interpret the decision in the context of the original claim.
there enough evidence at the \\( \\% \\) level of significance to the claim that the mean amount of lead in the air in u.s. cities is microgram per cubic meter.
(type integers or decimals. do not round )

Explanation:

Step1: Determine the significance level

The significance level $\alpha = 0.10$ (or 10%).

Step2: Analyze the decision about the null hypothesis

Since we failed to reject $H_0$ (the null hypothesis), this means there is not enough evidence.

Step3: Relate to the original claim

The original claim is that the mean amount of lead in the air in U.S. cities is less than 0.037 microgram per cubic meter. Failing to reject the null hypothesis (which would be the opposite of the claim in a one - tailed test where the claim is the alternative hypothesis) means we do not have enough evidence to support the claim.

Answer:

There is not enough evidence at the 10% level of significance to support the claim that the mean amount of lead in the air in U.S. cities is less than 0.037 microgram per cubic meter.