Question

2.) The tensile strength of a metal is a measure of its ability to resist tearing when it is pulled lengthwise. To see if a new experimental method of treating steel bars improves tensile strength, random samples of bars treated using the experimental method and treated using the old method are taken and the tensile strengths are measured and recorded (in newtons per square millimeter). Assume both populations are approximately normally distributed.

Experimental Method: 362 382 368 398 381 391 400 410 396 411 385 385 385

Old Method: 363 355 305 350 340 373 311 348 338 315

At significance level ? = .05, does the experimental treatment method increase mean tensile strength?

Answer 1

H0: Null Hypothesis: 0 ( the experimental treatment method does not increase mean tensile strength )

HA: Alternative Hypothesis: 0 ( the experimental treatment method increase mean tensile strength ) (Claim)

From the given data, the following statistics are calculated:

n1 = 13

1 = 388.7692

s1 = 14.4635

n2 = 10

2 = 339.8

s2 = 22.8561

=0.05

Pooled Standard Deviation is given by:

Test Statistic is given by:

df = 13 + 10 - 2 = 21

= 0.05

One Tail - Right Side Test

From Table, critical value of t = 1.7207

Since calculated value of t = 6.2823 is greatr than critical value of t = 1.7207, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the experimental treatment method increase mean tensile strength.