Which of the following equation is true?
1 answer:
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Answer:
Step-by-step explanation:
Hello!
Your study variable is
X: Number of students that finished tha statistics course with an a, in a sample of 100 students.
This variable has a binomial distribution X~Bi(n;ρ)
The student believes that no more than 20% of the students pass the course with an A. This percentage is the population proportion symbolically: ρ ≤ 0.20, and is your null hypothesis., so:
a.
H₀: ρ ≤ 0.20
H₁: ρ > 0.20
α: 0,01
The statistic to use is the Z approximation for the proportions. To assemble this statistic, the central limit theorem is applied, this theorem allows us, at a sufficiently large sample size (n≥30), to approximate the distribution of the sample proportion (^p) to normal:
^p ≈ N(p; p(1-p)(1/n))
The statistic formula is:
Z=<u> ^p - p </u>≈ N(0;1)
√p(1-p)(1/n)
the sample proportion is ^p= 0.24
b.
Z=<u> 0.24 - 0.2 </u>= 1
√0.2*0.8(1/100)
The rejection region of this hypothesis is one-tailed (positive) If you ever have trouble identifying the type of rejection region look at the direction of the alternative hypothesis, if it has the symbol < then is a one-tailed, to the left, rejection region. If it has the symbol > then is a one-tailed, to the right, rejection region and if it has the ≠ symbol, it means the rejection region is "split" in two, i.e. two-tailed.
The critical value is:
If Z ≥ 2.33, then you reject the null hypothesis.
If Z < 2.33, then you do not reject the null hypothesis.
The decision is to not reject the null hypothesis.
c.
The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
Symbolically:
P(Z ≥ 1) = 1 - P(Z < 1) = 1 - 0.84134 = 0.15866
You have to look at what is the probability of the calculated Z value, the direction of the p-value is always the same as the rejection region. In this case, is a one-tailed p-value (to the right)
Using the p-value approach, the decision rule is always the same:
If p-value ≤ α, then you reject the null hypothesis.
If p-value > α, then you don't reject the null hypothesis.
Since the p-value 0.15866 > 0.01, then you do not reject the null hypothesis.
As expected, using the two methods you reached the same decision. If not then you have to check your maths.
I hope it helped!
Answer:
The Area of the rectangle is 36
Step-by-step explanation:
One can use the vertices of the rectangle in coordinate form, by observing that (please see image attached):
(1) the distance between x-coordinates that share the same y-value give the length of the segments that define the horizontal sides of the rectangle,
(2) and the distance between y-coordinates that share the same x-value give the length of the segments that define the vertical sides of the rectangle,
Therefore, as an example of statement (1) above, the distance between the x-coordinates of : (-4,-3) and (-1,-3) which share the same "y-value" -3, is:
| -1 - (-4)| = |-1+4| = |3| = 3 which is the length of the horizontal side of the rectangle (the base of the rectangle).
As an example of statement (2), the distance between the y-coordinates of: ((-1,-3, and (-1,9) which share the same "x-value" -1, is:
| 9-(-3)| = |9+3|=|12|=12 which is the length of the vertical side of the rectangle (the height of the rectangle).
So, the area of the rectangle which is defined as the product of its base times its height, is given by:
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
<u /><u />
<u />
<u>Step 2: Solve for </u><em><u>v</u></em>
- Divide both sides by
:
Here we see that any value <em>v</em> greater than would work as a solution to the inequality.