Question

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.29 mg of mercury....

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.29 mg of mercury. A sample of 35 bulbs shows a mean of 3.38 mg of mercury.

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

1. H0: μ ≥ 3.29 mg vs. H1: μ < 3.29 mg
2. H0: μ ≤ 3.29 mg vs. H1: μ > 3.29 mg
3. H0: μ = 3.29 mg vs. H1: μ ≠ 3.29 mg
• a

• b

• c

(b) Assuming a known standard deviation of 0.20 mg, calculate the z test statistic to test the manufacturer’s claim. (Round your answer to 2 decimal places.)

Test statistic ________

(c) At the 1 percent level of significance (α = .01) does the sample exceed the manufacturer’s claim?

• Yes

• No

(d) Find the p-value. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.)

p-value ________

Solution:

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

H0: μ ≤ 3.29 mg vs. H1: μ > 3.29 mg

Q.(b)

Test statistic z = (M - )/[/n] = (3.38 - 3.29)/[0.20/35) = 2.66

Test statistic : 2.66

Q.(c)

= 0.01

For right tailed test , the critical value is

Test statistic 2.66 > critical value 2.33

We reject H0

Yes

Q.(d)

For right tailed test

p value = P(Z > z) = P(Z > 2.66) = 1 - P(Z < 2.66) = 1 - 0.9961 = 0.0039

p value = 0.0039

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