A new method was developed which makes a certain type of wood material tougher. An engineer selects a random sample of 25 pieces of wood treated using the new method and measures their hardness (variable X, unitless, assumed normal). The sample mean hardness is 173.8. The engineer hypothesizes that the mean hardness for wood pieces treated by the new method is greater than 170 compared with the hardness of 170 for untreated wood pieces. To investigate the engineer’s suggestion conduct the appropriate test for the mean hardness, μ, for the population of wood pieces treated using the new method. Assume that the population standard deviation is σ = 0.3. Required:
a. Conduct the test at a significance level of 0.05 using the rejection region method.
b. Calculate the confidence interval complementing.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true