An engineer wants to know if producing metal bars using a new experimental treat

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 a = 0.20, answer parts (a) through (e). Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem. (a) Identity the claim and state H_0 and H_a. The claim is "The new treatment (1) ___ in the tensile strength of the bars. What are H_0 and H_a? The null hypothesis, H_0, is (2) ___. The alternative hypothesis, H_a, is (3) ___. which hypothesis is the claim? The null hypothesis, H_0 The alternative hypothesis, H_a (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 needed.) Select the correct rejection region(s) below. a. -t_0

Explanation / Answer

x1bar = 388 ,s1 = 12.9099 , n1 = 7

x2bar = 413.3 , s2 = 25.68636 ,n2 = 10

s_pooled^2 = (s1^2*(n1-1) + s2^2(n2-1))/(n1+n2-2)

=( 12.91^2 * 6 + 9*25.68636^2)/15 = = 462.540

s_pooled= 21.5067

T = (x1bar- x2bar)/(s_pooled*sqrt(1/7+1/10))

=(388-413.3)/(21.5067*sqrt(1/7+1/10))

= -2.387

this follow t-distribution with 15 degree of freedom

t-critical = 1.341 for 20% level of significance

since |TS| > t-critical ,we reject the null hypothesis

4)there is enough evidence to support the claim

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---