Homework: Hypothesis Testing for Population Mean

1. Listed below are measured amounts of lead (in micrograms per cubic meter, or g/m) in the air. The EPA (Environmental Protection Survey Agency) has established an air quality standard for lead of 1.5 g/m. The measurements show below were recorded at Building 5 of the Word Trade Center site on different days immediately following the destruction caused by the terrorist attacks of September 11, 2001. After the collapse of the two World Trade Center buildings, there was considerable concern about the air quality. Use a 5% level of significance to test the claim that the average amount of lead in the air at the time exceeded 1.5 g/m.

5.40, 3.60, 2.82, 1.20, 0.85, 0.95, 1.10

A. Determine the Hypothesis:

Give the null and alternative hypothesis for this test in words and in math notation. Is this a left-tailed, right-tailed, or two-tailed? (Circle One)

B. Step 2: Collect the Data:

Determine the sample size, sample mean, and sample standard deviation. Is the sample mean consistent with the alternative hypothesis?

C. Assess the Evidence:

(i) Calculate the test statistic for the observed sample mean. Sketch the T distribution and identify the mean, standard error, and the position of the observed test statistic. Shade the area that represents the P-value.

(ii) Use the test statistic to find the P-value.

D. State a Conclusion:

(i) How does the P-value compare to the significance level? Should we reject or fail to reject the null hypothesis?

(ii) What can you conclude about the alternative hypothesis?

(iii) State a conclusion in the context of the problem.