Question

The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate a metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenters, so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Testing whether there is a difference in hardness readings between the steel ball and diamond specimens.

Specimen	1	2	3	4	5	6	7	8	9
Steel ball	50	57	61	71	68	54	65	51	53
Diamond	52	56	61	74	69	55	68	51	56

Project: find car rental prices for two car companies from 10 different cities for one week. Make sure the car is in the same class of cars.

Answer 1

Ans:

Specimen	1	2	3	4	5	6	7	8	9
Steel ball	50	57	61	71	68	54	65	51	53
Diamond	52	56	61	74	69	55	68	51	56
difference,d	-2	1	0	-3	-1	-1	-3	0	-3
d-bar=	-1.33333
sd=	1.5

Test statistic:

t=(-1.333-0)/(1.5/sqrt(9))

t=-2.667

df=9-1=8

p-value=tdist(2.667,8,2)=0.0285

As,p-value<0.05,reject the null hypothesis and we can conclude that there is a difference in hardness readings between the steel ball and diamond specimens