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.
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.
H_{0}: μ ≤ 3.29 mg vs. H_{1}: 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 H_{0}
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
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