The compressive strength, in kolipascals, was measured for concrete blocks made

Question

The compressive strength, in kolipascals, was measured for concrete blocks made of 6 different batches of concrete, both three and six days after pouring. The strength are presented in the following table.

Batch
1 2 3 4 5 6
After 3 days : 1341 1316 1352 1355 1327 1347
After 6 days 1376 1373 1366 1384 1358 1379

a)Can you conclude that the mean compressive strength after 6 days is greater than the compressive strength after 3 days? Use a = 0.05.

b)Construct a 95% confidence interval for the difference between the man speeds of the two processors?

c)Write down and check the assumptions of the procedures used above.

Explanation / Answer

a) Let x represent the mean and s the standard deviation

Let d=x6-x3

H0: d <=0

Ha: d >0

Test statistics: U= d / (sd2/nd)

Critical value: t(.05, 5)= 2.015

xd=33 and sd=13.871

U= (33)/((32.067))

U=5.827

U> 1.812 so we can reject the null hypothesis and conclude that the compressive strength after six days is significantly greater than the one after three days.

b) The confidence interval is:

[ xd - c (s2d/nd), xd + c (s2d/nd)]

c is t(.025, 5) = 2.571

[ 33 - (2.571(13.8712/6)), 33 + (2.571(13.8712/6))]

[33-14.559, 33+14.559]

[18.44, 47.559]

This 95% confidence interval confirms our previous findings in part a), as 0 is not included in the interval.

c) You assume unknown means and unequal& unknown variances.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.