Question

An engineer wants to know if the mean strengths of three different concrete mix designs differ significantly. He randomly selects 9 cylinders that measure 6 inches in diameter and 12 inches in height in which mixture A is​ poured, 9 cylinders of mixture​ B, and 9 cylinders of mixture C. After 28​ days, he measures the strength​ (in pounds per square​ inch) of the cylinders. The results are presented in the accompanying table.

Mixture A   Mixture B   Mixture C
3,960   4,070   4,150
4,040   4,350   3,820
3,780   4,620   4,040
3,890   3,730   4,150
3,990   4,890   4,190
4,090   4,120   3,800
3,830   4,640   3,750
3,940   4,160   3,990
4,080   3,850   4,320

​(a) State the null and alternative hypotheses. Choose the correct answer below.

B.H0: μA=μB=μC and H1: at least one of the means is different

Correct Answer

​(b) Explain why we cannot use​ one-way ANOVA to test these hypotheses. Choose the correct answer below.

A.

Because populations are not normally distributed.

B.

Because the standard deviation for mixture B is more than two times larger than the standard deviation for mixture A.

C.

Because the samples are not random.

D.

Because the samples are not independent of each other.

Answer 1