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 0.067 microgram per cubic meter. at α = 0.01, 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 h₀ 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: Understand the hypothesis test result

Since we failed to reject the null hypothesis \(H_0\), it means we do not have sufficient evidence to support the alternative hypothesis. The alternative hypothesis here is the claim that the mean amount of lead in the air in U.S. cities is less than \(0.037\) microgram per cubic meter.

Step2: Fill in the blanks based on the hypothesis - test result

When we fail to reject \(H_0\), we say there is not enough evidence. The significance level \(\alpha = 0.01=1\%\). And we are testing the claim that the mean is less than \(0.037\)

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.