The paint used to make 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 will be based on a random sample of size n from a normal population distribution. what conclusion is appropriate in each of the following situations? (round your p-values to three decimal places.) (a) n = 13, t = 3.2, α = 0.05

We conclude that average reflectometer reading for a new type of paint is greater than 20

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 20

Sample size, n = 13

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

Formula:

Degree of freedom = n - 1 = 13 - 1 = 12

Now, we calculate the p-value with the help of standard table.

P-value = 0.004

Since, the p-value is less than the significance level, we fail to accept the null hypothesis and reject it.

Thus, there is enough evidence to support that average reflectometer reading for a new type of paint is greater than 20

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

answer:   b

step-by-step explanation:

x2 = 16

x can not be a negative number because 16 is positive

the only answer would be positive 8