8) The active ingredient in antiseptic liquid bandages is 8-hydroxyquinoline (8h). This chemical can be harmful through simple skin contact, by swallowing, or inhalation. Suppose the list of ingredients on a 3M Nexcare liquid bandage indicates that the volume of 8h is 1%. A random sample of eight bottles of this product was obtained, and each was analyzed to obtain the volume of 8h. The sample mean was
x = 1.025%.
Assume the underlying population is normal and
σ = 0.04.
Is there any evidence to suggest that the true mean percentage of 8h is different from 1%? Use α = 0.01.
a) Calculate the test statistic. (Round your answer to two decimal places.)
z =
b)Compute the p value. (Round your answer to four decimal places.)
Solution:
σ = 0.04
= 1.025
n = 8
H0 :
= 1
H1 :
1
Use α = 0.01
a)
The test statistic z is given by
z =
= (1.025 - 1) / (0.04/8)
= 1.77
The test statistic z = 1.77
b) Now , observe that ,there is
sign in H1. So , the test is two tailed.
For two tailed test
p value = 2 * P(Z < -z)
= 2 * P(Z < -1.77)
= 2 * 0.0384
= 0.0768
p value = 0.0768
The p value is greater than α = 0.01
So , Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true mean percentage of 8h is different from 1%
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