An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars (the ability to resist tearing when pulled lengthwise). At =0.05,

answer parts (a) through (e). Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem.

Treatment

Tensile strengths (newtons per square millimeter)

Experimental

391

371

449

439

363

388

384

Conventional

369

424

431

445

352

440

397

427

423

431

(a) Identify the claim and state

H0

and

Ha.

The claim is "The new treatment

makes a difference

does not make a difference

in the tensile strength of the bars."

What are

H0

and

Ha?

The null hypothesis,

H0,

is

mu 1 equals mu 21=2

mu 1 less than or equals mu 212

mu 1 greater than or equals mu 212

.

The alternative hypothesis,

Ha,

is

mu 1 not equals mu 212

mu 1 greater than mu 21>2

mu 1 less than mu 21<2

.

Which hypothesis is the claim?

The alternative hypothesis, Ha

The null hypothesis, H0

(b) Find the critical value(s) and identify the rejection region(s).

Enter the critical value(s) below.

enter your response here

(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)

Select the correct rejection region(s) below.

A.

t>t0

B.

t0

C.

tt0

D.

t

(c) Find the standardized test statistic.

t=enter your response here

(Type an integer or decimal rounded to the nearest thousandth as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

Fail to reject

Reject

the null hypothesis.

(e) Interpret the decision in the context of the original claim.

At the

5%

significance level,

there is not

there is

enough evidence to support the claim.