Question

Find the test statistic & decide whether to fail to reject or reject.

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 a = 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 427 377 417 440 431 423 414 Conventional 441 399 353 414 359 401 385 421 384 423 (C) Find the standardized test statistic. t= (Type an integer or decimal rounded to the nearest thousandth as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. the null hypothesis.

Answer 1

Here as we can use technology, we will use t test for two sample means for equal variances.

Here is the summary

t-Test: Two-Sample Assuming Equal Variances
	Experimental	Conventional
Mean	418.4285714	398
Variance	409.2857143	797.7777778
Observations	7	10
Pooled Variance	642.3809524
Hypothesized Mean Difference	0
df	15
t Stat	1.635559053
P(T<=t) one-tail	0.061368656
t Critical one-tail	1.340605608
P(T<=t) two-tail	0.122737312
t Critical two-tail	1.753050325

Test statistic

t = 1.636

(d) as alpha = 0.10 and the test is two tailed so we would fail to reject the null hypothesis.