## Help with Hyphothesis Testing Problems

So yeah, i've come across a few questions that I have no idea how to do, wasn't covered in class and the book doesn't help, or I simply don't understand them. No one else on the floor knows how to do them, math help lab is closed, and the homework is due in one hour...

(1) Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 30 psi. Let μ denote the true average pressure. Find the P-value associated with each of the following given z statistic values for testing H0: μ = 30 versus Ha: μ 30 when σ is known. (Give the answers to four decimal places.)

(a) z = 2.35
P = ????

(2) Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let μ denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: μ = 20 versus Ha: μ > 20 based on a sample of 20 observations gave t = 3.0. What conclusion is appropriate at each of the following significance levels?

(a)
α = .05

Reject or fail to reject?

(3) A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. The relevant hypotheses are H0: μ = 10 versus Ha: μ < 10.

(a) If t = -2.3 and α = .05 is selected, what conclusion is appropriate?

Reject or fail to reject?

(4) In a survey of 526 U.S. businesses, 400 of these companies indicated that they monitor employees' web site visits. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of businesses in the United States.

(figured out a, but B is uh...)

(a) Is there sufficient evidence to conclude that more than 75% of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01. (For z give the answer to two decimal places. For P give the answer to four decimal places.)

Z = .55
P = .2899

(b) Is there sufficient evidence to conclude that a majority of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01. (For z give the answer to two decimal places. For P give the answer to four decimal places.)

Z = ???
P = ???

Help!