Suppose you are testing the sample is large (n = 71) and the variance, σ2, is known. h0: μ=20 vs h1: μ> 20. (a) find the critical value(s) corresponding to α = 0.08. (b) you find that z = 1.56. based on your critical value, what decision do you make regarding the null hypothesis (i.e. do you reject h0 or do not reject h0)?

We reject the null hypothesis.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 71

Alpha, α = 0.08

Population variance is known.

First, we design the null and the alternate hypothesis

We use One-tailed z test to perform this hypothesis.

Formula:

a) We calculate the z-critical with the help of z-table.

b)

Since,  

We fail to accept the null hypothesis and reject the null hypothesis and accept the alternate hypothesis.

Y = -x² + 4
y = 2x + 1

Since the right side of both sides are equal to y, we can set them equal.

-x² + 4 = 2x + 1

Now that we just have one variable, we can solve easily.
Let's get everything on one side.

x² + 2x - 3 = 0

Let's solve this quadratic by factoring.
We want two numbers that multiply to -3 and add to 2.
These are 3 and -1. Let's split the middle.

x² - x + 3x - 3 = 0

Factor the first and last two terms...

x(x-1) + 3(x-1) = 0
(x+3)(x-1) = 0

And value of x which causes either factor to equal 0 is a solution.
We can derive these equations:

x+3=0 and x-1=0
Then solving for x...
x = -3 or 1