Question

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=0.10, 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 | 392 445 397 449 389 440 376
conventional | 354 357 385 354 364 394 404 391 438 443
(a) identify the claim and state h₀ and hₐ.
the claim is \the new treatment makes a difference in the tensile strength of the bars.\
what are h₀ and hₐ?
the null hypothesis, h₀, is dropdown. the alternative hypothesis, hₐ, is dropdown.

Explanation:

Step1: Define Hypotheses

The null hypothesis \( H_0 \) assumes no difference between the two treatments, so \( H_0: \mu_1 = \mu_2 \) (where \( \mu_1 \) is the mean tensile strength for experimental, \( \mu_2 \) for conventional). The alternative hypothesis \( H_a \) reflects the claim of a difference, so \( H_a: \mu_1
eq \mu_2 \).

Answer:

The null hypothesis, \( H_0 \), is \( \boldsymbol{\mu_1 = \mu_2} \). The alternative hypothesis, \( H_a \), is \( \boldsymbol{\mu_1
eq \mu_2} \).