GreenBeam Limited claims that its compact fluorescent bulbs average no more than 3.27 mg of mercury. A sample of 65 bulbs shows a mean of 3.34 mg of mercury.

(a) State the hypotheses for a right-tail test, using GreenBeam's claim as the null hypothesis about the mean.

(b) Assuming a known standard deviation of 0.21 mg, calculate the z test statistic to test the manufacturer's claim. (c) At the 5 percent level of significance (a = .05) does the sample exceed the manufacturer's claim?

(d) find the p-value.