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
choose the graph which shows the rejection region.
(c) find the standardized test statistic, t
the standardized test statistic is \\( t = 0.11 \\)
(round to two decimal places as needed)
(d) decide whether to reject or fail to reject the null hypothesis.
\\( \square h _ { 0 } \\) because the standardized test statistic \\( \square \\) in the rejection region
(e) interpret the decision in the context of the original claim.
there \\( \square \\) enough evidence at the \\( \square \\% \\) level of significance to \\( \square \\)
the claim that the mean amount of lead in the air in u.s. cities is
\\( \square \\) microgram per cubic meter.
(type integers or decimals. do not round)

Explanation:

Step1: Determine the significance level

The significance level $\alpha = 0.01$ or $1\%$.

Step2: Analyze the decision about the null hypothesis

Since we failed to reject $H_0$ (the null hypothesis).

Step3: Interpret in the context of the claim

When we fail to reject the null hypothesis, it means there is not enough evidence to support the alternative 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.

Answer:

There is not enough evidence at the $1\%$ 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.