At 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.
<h3>How to state hypothesis conclusion?</h3>
We are given;
Sample size; n = 78
population standard deviation σ = 37
Sample Mean; x' = 280
Population mean; μ = 287
The school administrator declares that mean score is more (bigger than) 280. Thus, the hypotheses is stated as;
Null hypothesis; H₀: μ > 280
Alternative hypothesis; Hₐ: μ < 280
This is a one tail test with significance level of α = 0.13
From online tables, the critical value at α = 0.13 is z(c) = -1.13
b) Formula for the test statistic is;
z = (x- μ)/(σ/√n)
z = ((280 - 287) *√78 )/37
z = -1.67
c) From online p-value from z-score calculator, we have;
P[ z > 280 ] = 0.048
d) The value for z = -1.67 is smaller than the critical value mentioned in problem statement z(c) = - 1.13 , the z(s) is in the rejection zone. Therefore we reject H₀
e) We conclude that at 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.
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Answer:
If an item is x dollars and 20% discount is applied, the new price will be: 0.8x
Step-by-step explanation:
100 - 20%(20) = 80
80 = 80% or 0.8
So, the remaining of the price of x will be 0.8x.
Answer:
5 feet & 15 feet
Step-by-step explanation:
<em>The question is to find the lengths of 2 sides of the rectangle</em>.
<u>Solution:</u>
Let shorter side be "x"
Let longer side be "y"
From the question, we can write:
y = 3x
also
y - x = 10
Now, putting the first on second equation, we get:
y - x = 10
3x - x = 10
2x = 10
x = 10/2 = 5
Now, y = 3x, y = 3(5) = 15
So we can say the lengths of 2 sides of the rectangle is 5 feet & 15 feet
Let us try and solve it analytically. We have that the side=x+3 together with the short side=s and the diagonal=x+4 satisfy the Pythagorean Theorem. Then we have that
. This yields
which yields s^2=2x+7, hence a) is the correct answer.
