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 α=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 443 376 431 439 398 368 360 Conventional 392 392 400 425 372 370 439 366 392 381 (a) Identify the claim and state H0 and Ha. The claim is "The new treatment makes a difference 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 2μ1=μ2 mu 1 equals mu 2μ1=μ2 mu 1 less than or equals mu 2μ1≤μ2 mu 1 greater than or equals mu 2μ1≥μ2 . The alternative hypothesis, Ha, is mu 1 not equals mu 2μ1≠μ2 mu 1 not equals mu 2μ1≠μ2 mu 1 greater than mu 2μ1>μ2 mu 1 less than mu 2μ1<μ2 . Which hypothesis is the claim? The null hypothesis, H0 The alternative hypothesis, Ha (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. 2.1312.131 (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. t>t0 C. t<−t0, t>t0 D. −t0

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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

α=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

443

376

431

439

398

368

360

Conventional

392

400

425

372

370

439

366

392

381

(a) Identify the claim and state

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

and

Ha?

The null hypothesis,

H0,

mu 1 equals mu 2μ1=μ2

mu 1 less than or equals mu 2μ1≤μ2

mu 1 greater than or equals mu 2μ1≥μ2

The alternative hypothesis,

Ha,

mu 1 not equals mu 2μ1≠μ2

mu 1 greater than mu 2μ1>μ2

mu 1 less than mu 2μ1<μ2

Which hypothesis is the claim?

The null hypothesis, H0

The alternative hypothesis, Ha

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

Enter the critical value(s) below.

2.1312.131

(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.

t<−t0

t>t0

t<−t0, t>t0

−t0<t<t0

t=nothing

(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

significance level,

there is not

there is

enough evidence to support the claim.

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