Question

A product developer is investigating the tensile strength of a new synthetic fiber that will be used
to make cloth for men's shirts. Strength is usually affected by the percentage of cotton used in the
blend of material for the fiber. The engineer conducts a completely randomized experiment with
five levels of cotton and replicates the experiment five time. The data are shown bellow
	Cotton weight percent
Observation	15	20	25	30	35
1	7	12	14	19	7
2	7	17	19	25	10
3	15	12	19	22	11
4	11	18	18	19	15
5	9	18	18	23	11

a) Is there evidence to support the claim that cotton content affects the mean tensile strength at a = 0.05?

b) Is there a significance difference in a percent conent among the groups? What would be the percent content that you would recommend? Justify your answer

Answer 1

a)

We will do One way ANOVA:

Null hypothesis

Alternate hypothesis HA : At least one of the mean is not equal.

Significance level = 0.05

F- value = 14.75

P- value = 0.000000913

F- critical = 2.866

Since P value (0.000000913) is less than the significance level(0.05) so we have to reject the null hypothesis.

From this we can conclude that at least one of the mean of tensile strength for different cotton is not equal to other, so that means cotton content affects the mean tensile strength.

b)

Yes, there is a significance difference in a percent content among the groups the F-value is 14.76 with a corresponding P-value of 0.000. The percentage of cotton in the fiber appears to have an affect on the tensile strength.