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). 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
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
(b) find the critical value(s) and identify the rejection region(s).
enter the critical value(s) below.
(type an integer or decimal rounded to three decimal places as needed. use a comma to separate answers as ne

Explanation:

Step1: Determine sample sizes

Experimental sample size \( n_1 = 7 \), Conventional sample size \( n_2 = 10 \). Degrees of freedom \( df = n_1 + n_2 - 2 = 7 + 10 - 2 = 15 \).

Step2: Identify test type and significance level

Two - tailed test (since \( H_a: \mu_1
eq\mu_2 \)) with \( \alpha = 0.10 \), so \( \alpha/2=0.05 \).

Step3: Find critical values

Using t - distribution table or calculator, for \( df = 15 \) and \( \alpha/2 = 0.05 \), the critical values are \( \pm 1.753 \).

Answer:

\( - 1.753, 1.753 \)