Question

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.)

Answer #1

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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