1a) The strength of concrete depends to some extent on the method used for drying it. Two different drying methods were tested independently on specimens. The strength using each of the methods follow a normal distribution with mean μ_x and μ_y respectively and the same variance. The results are:
method 1: n1=7, x bar=3250, s1=210
method 2: n2=10, y bar=3240, s2=190
Do the methods appear (use alpha=0.05) to produce concrete with different mean strength ?
For this one, the test is H_o: μ_x=μ_y v.s. H_a: μ_x≠μ_y. I computed a p-value of >0.2, so the p-value is greater than alpha(which is 0.05), and so we fail to reject H_o and the answer is "no".
Now I am stuck with part b...
1b) Suppose σ_x=210, σ_y=190 (n1, n2, x bar, y bar same as part a). Find the probability of deciding that the methods are not different when the true difference in means is 2.
I am having trouble understanding what the question is asking for. Is it asking for P(type II error)? If so, how can I find it in this case?
Any help is greatly appreciated!
P.S. By the way, this topic is also discussed in SOS mathematics cyberboard forum.