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%