Question

Determine whether there is there a protective effects of oil supplements, argan oil (AO) and coconut oil (CO) in hair dyes on hair tensile strength and porosity?

Data: Tensile strength of hair in Mpa (megapascals)

AO: 12, 9, 13, 14, 8, 16, 11, 12

CO: 13, 15, 11, 8, 15, 16, 12,14

Control:  8, 9, 13, 7, 8, 6, 10, 11

Identify the independent variable

Identify the dependent variable

Identify the control group

Calculate the means for each group (AO, CO, and control)

Indicate the ranges for each group (AO, CO, and control)

Indicate the medians for each group (AO, CO and control)

Indicate the mode for each group (AO, CO, and control)

Calculate the standard deviation for each group (AO, CO and control)?

Degrees of freedom

Indicate the type of t-test used

Perform t-test

Find the p-value

Write a conclusion for the experiment.

Answer 1

Answer :

Here, given data of  Tensile strength of hair in Mpa (megapascals)

1) for given data ,

independent variable= Argan oil (AO) and Coconut oil (CO)

dependent variable= Control

2) By using Excel ,

	AO	CO	Control
	12	13	8
	9	15	9
	13	11	13
	14	8	7
	8	15	8
	16	16	6
	11	12	10
	12	14	11
mean	11.875	13	9
median	12	13.5	8.5
mode	12	15	8
variance	6.696429	6.857143	5.142857
standard deviation	2.587746	2.618615	2.267787

now ,

Mean of AO is 11.875 , CO is 13 and control is 9 .

Ranges of  AO is (8 to 16) , CO is (8 to 16) and control is (8 to 13) .

Median of AO is 12 , CO is 13.5 and control is 8.5 .

mode of AO is 12 , CO is 15 and control is 8 .

Standard deviation of AO is 2.587746 , CO is 2.618615  and control is  2.267787.

2) t- test using Excel :

	AO	CO
Mean	11.875	13
Variance	6.696429	6.857143
Observations	8	8
Hypothesized Mean Difference	0
df	14
t Stat	-0.86431
P(T<=t) one-tail	0.200991
t Critical one-tail	1.76131
P(T<=t) two-tail	0.401983
t Critical two-tail	2.144787

From above calculations :

test statistic < critical value , Hence we concude that there is not significant difference between argan oil (AO) and coconut oil (CO) in hair dyes on hair tensile strength and porosity.

and

P-value for t-test is

Unequal Variances
DF : 13
95% Confidence Interval for the Difference ( -3.937 , 1.687 )
Test Statistic t = -0.8643
Population 1 ≠ Population 2: P-Value = 0.403
Population 1 < Population 2: P-Value = 0.7985
Population 1 > Population 2: P-Value = 0.2015

Conclusion :

p-value > 0.05 ( level of significance) , hence we accept H0 at 5 % level of significance.

RESULT :

There is not significant difference between argan oil (AO) and coconut oil (CO) in hair dyes on hair tensile strength and porosity.