Let μ denote the true average tread life of a certain type of tire. Consider testing H0 : μ =20000 versus Ha : μ >20000 based on a sample of size n = 16 from a normal population distribution with σ = 1500. A test with α = .01 is used. (z.01 = 2.33, z.1 = 1.28) (a) If ¯ x = 20960, what is the decision? (b) What is the probability of making a type II error when μ = 21000? (c) If it is also required that β (21000)=.1, what sample size n is necessary?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

i believe it is 0.1m because the measurement of 30.4m limits how precise you can be

you can only be as precise as the least precise measurement

sorry not knowing about that