The Occupational Safety and Health Act (OSHA)

allows issuance of engineering standards to ensure safe workplaces for all Americans. The maximum allowable mean level of arsenic in smelters, herbicide production facilities, and other places where arsenic is used is

.004 milligram per cubic meter of air. Suppose smelters at two plants are being investigated to determine whether they are meeting OSHA standards. Two analyses of the air are made at each plant, and the results (in milligrams per cubic meter of air) are shown in the table.

Plant 1 Plant 2 ..............................................................................................................

Observation Arsenic Level Observation Arsenic Level ..............................................................................................................

1 .01 1 .05 2 .005 2 .09

a. What are the appropriate null and alternative hypotheses if we wish to test whether the plants meet the current OSHA standard?

b. These data are analyzed by MINITAB, with the results as shown on p. 326. Check the calculations of the t statistics and p-values.

c. Interpret the results of the two tests.

x6.53 For the binomial sample sizes and null hypothesized values of p in each part, determine whether the sample size is large enough to use the normal approximation methodology presented in this section to conduct a test of the null hypothesis H,: p = p,.

a. n = 900, p, = 975

b. n = 125, p, = .O1

c. n = 40, p, = .75

d. n = 15, p,, = .75

e. n = 12, p, = .62