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 \\( \alpha = 0.02 \\), answer parts (a) through (e). assume the population variances are equal and the samples are random. if convenient, use technology to solve the problem.

\

$$\begin{tabular}{l|l} treatment & tensile strengths (newtons per square millimeter) \\\\ \\hline experimental & 365 353 432 363 385 413 386 \\\\ conventional & 444 394 411 374 389 362 350 416 434 447 \\\\ \\end{tabular}$$

(a) identify the claim and state \\( h _ { 0 } \\) and \\( h _ { a } \\).

the claim is \the new treatment makes a difference in the tensile strength of the bars.\

what are \\( h _ { 0 } \\) and \\( h _ { a } \\)?

the null hypothesis, \\( h _ { 0 } \\), is \\( \mu _ { 1 } = \mu _ { 2 } \\). the alternative hypothesis, \\( h _ { a } \\), is \\( \mu _ { 1 } \
eq \mu _ { 2 } \\).

which hypothesis is the claim?

\\( \bigcirc \\) the null hypothesis, \\( h _ { 0 } \\)
\\( \bigcirc \\) the alternative hypothesis, \\( h _ { a } \\)

Explanation:

The claim is that there is a difference in tensile strength, which is represented by the alternative hypothesis \(H_a:\mu_1
eq\mu_2\). The null hypothesis \(H_0:\mu_1 = \mu_2\) assumes no difference. Since the claim is about a difference (not equality), it aligns with the alternative hypothesis.

Answer:

The alternative hypothesis, \(H_a\)