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. (use a comma to separate answers as needed. round to two decimal places as needed.) choose the graph which shows the rejection region. (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. $h_0$ because the standardized test statistic in the rejection region.

Explanation:

Step1: Determine the type of test

Since the claim is that the mean is less than a certain value, this is a left - tailed test.

Step2: Analyze the rejection region

For a left - tailed \(t\) - test, the rejection region is \(t < t_0\).

Step3: Analyze the test statistic

The standardized test statistic \(t = 0.22\).

Step4: Compare the test statistic with the rejection region

Since \(0.22>t_0\) (for a left - tailed test at \(\alpha = 0.10\) with \(n-1=57 - 1=56\) degrees of freedom, \(t_0\approx - 1.296\)), the test statistic is not in the rejection region.

Answer:

Fail to reject \(H_0\) because the standardized test statistic is not in the rejection region.