Most water treatment facilities monitor the quality of their drinking water on an hourly basis. one variable measured is ph, which measures the degree of alkalinity or acidity in the water. a ph below 7.0 is acidic, one above 7.0 is alkaline, and a ph of 7.0 is neutral. one water-treatment plant has a target ph of 8.5. (most try to maintain a slightly alkaline level) the mean and standard deviation of 1 hour test results based on 49 water samples at this plant are: = 8.42; s = 0.16 does this sample provide sufficient evidence that the mean ph level in the water differs from 8.5?

There is not enough evidence to conclude that the mean pH level is 8.5.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 8.5

Sample mean, = 8.42

Sample size, n = 49

Alpha, α = 0.05

Sample standard deviation, s = 0.16

First, we design the null and the alternate hypothesis

We use two-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since, the test statistic does not lies in the acceptance region, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

There is not enough evidence to conclude that the mean pH level is 8.5.

table 3 represents a direct variation function. : )

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