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 μ₁=μ₂. the alternative hypothesis, hₐ, is μ₁≠μ₂.
which hypothesis is the claim?
○ the null hypothesis, h₀
○ the alternative hypothesis, hₐ

Explanation:

The claim is that the new treatment makes a difference in tensile strength, which means the means of the two treatments (experimental and conventional) are not equal. The alternative hypothesis \( H_a: \mu_1
eq \mu_2 \) represents a difference, while the null hypothesis \( H_0: \mu_1 = \mu_2 \) represents no difference. So the claim matches the alternative hypothesis.

Answer:

The alternative hypothesis, \( H_a \)