Question

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 ________

Answer 1

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

Answer is

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