Question

For your senior design project one of the problems you had to work on was the yield strength of a steel weld joint created by a robot. Your test 15 weld joints and found they had an average yield strength of 270 MPa with a standard deviation of 25MPa. Give a 95% confidence interval for the true yield strength of the weld joint. (by the way Mpa is megapascals measure of force in metric units. 1MPa =145.038 psi)

A. give the null and alternative hypotheses

B Give the critical values of the test

C. Give the test statistic

D. Give the p value

E. Give the type of error you could have made

Using the data in problem above test to see if the yield strength of the robotically welded join is equal to the minimum yield strength for steel, 295 MPa, or is it less. Test at a=0.05.

A. give the null and alternative hypotheses

B Give the critical values of the test

C. Give the test statistic

D. Give the p value

E. Give the type of error you could have made

Answer 1

Solution1:

95% confidence interval for the true yield strength of the weld joint

=xbar-tc*s/sqrt(n),xbar+tc*s/sqrt(n)

n=15

sample sddev=s=25

sample mean=xbar=270

df=n-1=15-1=14

alpha=0.05

alpha/2=0.025

t critcal=T.INV(0.025;14)=2.144786688

substituting these values we get

270-2.14479*25/sqrt(15),270+2.14479*25/sqrt(15)

256.1554,283.8446

95% lower limit= 256.1554

95% upper limit=283.8446

Solution2:

A. give the null and alternative hypotheses

Ho:mu<=295

Ha:mu>295

B Give the critical values of the test

n=15

alpha=0.05

alpha/2=0.05/2=0.025

df=n-1=15-1=14

t crit==T.INV(0.05;14)=1.761310136

C. Give the test statistic

t=xbar-mu/s/sqrt(n)

=(270-295)/(25/sqrt(15))

t =-3.872983

D. Give the p value

p=T.DIST.RT(-3.872983;14)

p=0.999155363

p=0.9992(rounding to 4 decimals)

p>0.05

Do not reject Ho.